Simplify (a/(1+a)+(1-a)/a)/(a/(a-1)-(1+a)/a)

$\frac{\frac{a}{1 + a} + \frac{1 - a}{a}}{\frac{a}{a - 1} - \frac{1 + a}{a}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $(1 + a) a (a - 1)$ .

Multiply $\frac{\frac{a}{1 + a} + \frac{1 - a}{a}}{\frac{a}{a - 1} - \frac{1 + a}{a}}$ by $\frac{(1 + a) a (a - 1)}{(1 + a) a (a - 1)}$ .

$\frac{(1 + a) a (a - 1)}{(1 + a) a (a - 1)} \cdot \frac{\frac{a}{1 + a} + \frac{1 - a}{a}}{\frac{a}{a - 1} - \frac{1 + a}{a}}$

Combine.

$\frac{(1 + a) a (a - 1) (\frac{a}{1 + a} + \frac{1 - a}{a})}{(1 + a) a (a - 1) (\frac{a}{a - 1} - \frac{1 + a}{a})}$

Step 2

Apply the distributive property.

$\frac{(1 + a) a (a - 1) \frac{a}{1 + a} + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $1 + a$ .

Factor $1 + a$ out of $(1 + a) a (a - 1)$ .

$\frac{(1 + a) (a (a - 1)) \frac{a}{1 + a} + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Cancel the common factor.

$\frac{(1 + a) (a (a - 1)) \frac{a}{1 + a} + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Rewrite the expression.

$\frac{a (a - 1) a + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Raise $a$ to the power of $1$ .

$\frac{a^{1} a (a - 1) + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Raise $a$ to the power of $1$ .

$\frac{a^{1} a^{1} (a - 1) + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{1 + 1} (a - 1) + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Add $1$ and $1$ .

$\frac{a^{2} (a - 1) + (1 + a) a (a - 1) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Cancel the common factor of $a$ .

Factor $a$ out of $(1 + a) a (a - 1)$ .

$\frac{a^{2} (a - 1) + a ((1 + a) (a - 1)) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Cancel the common factor.

$\frac{a^{2} (a - 1) + a ((1 + a) (a - 1)) \frac{1 - a}{a}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Rewrite the expression.

$\frac{a^{2} (a - 1) + (1 + a) (a - 1) (1 - a)}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Factor $- 1$ out of $a$ .

$\frac{a^{2} (a - 1) + (1 + a) (- 1 (- a) - 1) (1 - a)}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{a^{2} (a - 1) + (1 + a) (- 1 (- a) - 1 (1)) (1 - a)}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Factor $- 1$ out of $- 1 (- a) - 1 (1)$ .

$\frac{a^{2} (a - 1) + (1 + a) (- 1 (- a + 1)) (1 - a)}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Reorder terms.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 (- a + 1) (- a + 1)}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Raise $- a + 1$ to the power of $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 ({(- a + 1)}^{1} (- a + 1))}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Raise $- a + 1$ to the power of $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 ({(- a + 1)}^{1} {(- a + 1)}^{1})}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{1 + 1}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Add $1$ and $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a (a - 1) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Cancel the common factor of $a - 1$ .

Factor $a - 1$ out of $(1 + a) a (a - 1)$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(a - 1) ((1 + a) a) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Cancel the common factor.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(a - 1) ((1 + a) a) \frac{a}{a - 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Rewrite the expression.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a \cdot a + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Raise $a$ to the power of $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) (a^{1} a) + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Raise $a$ to the power of $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) (a^{1} a^{1}) + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{1 + 1} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Add $1$ and $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (1 + a) a (a - 1) (- \frac{1 + a}{a})}$

Cancel the common factor of $a$ .

Move the leading negative in $- \frac{1 + a}{a}$ into the numerator.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (1 + a) a (a - 1) \frac{- (1 + a)}{a}}$

Factor $a$ out of $(1 + a) a (a - 1)$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + a ((1 + a) (a - 1)) \frac{- (1 + a)}{a}}$

Cancel the common factor.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + a ((1 + a) (a - 1)) \frac{- (1 + a)}{a}}$

Rewrite the expression.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (1 + a) (a - 1) (- (1 + a))}$

Raise $1 + a$ to the power of $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- ({(1 + a)}^{1} (1 + a)))}$

Raise $1 + a$ to the power of $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- ({(1 + a)}^{1} {(1 + a)}^{1}))}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{1 + 1})}$

Add $1$ and $1$ .

$\frac{a^{2} (a - 1) + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{a^{2} a + a^{2} \cdot - 1 + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a^{2}$ by $a$ by adding the exponents.

Multiply $a^{2}$ by $a$ .

Raise $a$ to the power of $1$ .

$\frac{a^{2} a^{1} + a^{2} \cdot - 1 + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{2 + 1} + a^{2} \cdot - 1 + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Add $2$ and $1$ .

$\frac{a^{3} + a^{2} \cdot - 1 + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Move $- 1$ to the left of $a^{2}$ .

$\frac{a^{3} - 1 \cdot a^{2} + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Rewrite $- 1 a^{2}$ as $- a^{2}$ .

$\frac{a^{3} - a^{2} + (1 + a) \cdot - 1 {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Apply the distributive property.

$\frac{a^{3} - a^{2} + (1 \cdot - 1 + a \cdot - 1) {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- 1$ by $1$ .

$\frac{a^{3} - a^{2} + (- 1 + a \cdot - 1) {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Move $- 1$ to the left of $a$ .

$\frac{a^{3} - a^{2} + (- 1 - 1 \cdot a) {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Rewrite $- 1 a$ as $- a$ .

$\frac{a^{3} - a^{2} + (- 1 - a) {(- a + 1)}^{2}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Rewrite ${(- a + 1)}^{2}$ as $(- a + 1) (- a + 1)$ .

$\frac{a^{3} - a^{2} + (- 1 - a) ((- a + 1) (- a + 1))}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Expand $(- a + 1) (- a + 1)$ using the FOIL Method.

Apply the distributive property.

$\frac{a^{3} - a^{2} + (- 1 - a) (- a (- a + 1) + 1 (- a + 1))}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Apply the distributive property.

$\frac{a^{3} - a^{2} + (- 1 - a) (- a (- a) - a \cdot 1 + 1 (- a + 1))}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Apply the distributive property.

$\frac{a^{3} - a^{2} + (- 1 - a) (- a (- a) - a \cdot 1 + 1 (- a) + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$\frac{a^{3} - a^{2} + (- 1 - a) (- 1 \cdot - 1 a \cdot a - a \cdot 1 + 1 (- a) + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (- 1 \cdot - 1 (a \cdot a) - a \cdot 1 + 1 (- a) + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a$ by $a$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (- 1 \cdot - 1 a^{2} - a \cdot 1 + 1 (- a) + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- 1$ by $- 1$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (1 a^{2} - a \cdot 1 + 1 (- a) + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a^{2}$ by $1$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (a^{2} - a \cdot 1 + 1 (- a) + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- 1$ by $1$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (a^{2} - a + 1 (- a) + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- a$ by $1$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (a^{2} - a - a + 1 \cdot 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $1$ by $1$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (a^{2} - a - a + 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Subtract $a$ from $- a$ .

$\frac{a^{3} - a^{2} + (- 1 - a) (a^{2} - 2 a + 1)}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Expand $(- 1 - a) (a^{2} - 2 a + 1)$ by multiplying each term in the first expression by each term in the second expression.

$\frac{a^{3} - a^{2} - 1 a^{2} - 1 (- 2 a) - 1 \cdot 1 - a \cdot a^{2} - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Simplify each term.

Rewrite $- 1 a^{2}$ as $- a^{2}$ .

$\frac{a^{3} - a^{2} - a^{2} - 1 (- 2 a) - 1 \cdot 1 - a \cdot a^{2} - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- 2$ by $- 1$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 \cdot 1 - a \cdot a^{2} - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- 1$ by $1$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a \cdot a^{2} - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - (a^{2} a) - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a^{2}$ by $a$ .

Raise $a$ to the power of $1$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - (a^{2} a^{1}) - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a^{2 + 1} - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Add $2$ and $1$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a^{3} - a (- 2 a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Rewrite using the commutative property of multiplication.

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a^{3} - 1 \cdot - 2 a \cdot a - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a^{3} - 1 \cdot - 2 (a \cdot a) - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $a$ by $a$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a^{3} - 1 \cdot - 2 a^{2} - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- 1$ by $- 2$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a^{3} + 2 a^{2} - a \cdot 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Multiply $- 1$ by $1$ .

$\frac{a^{3} - a^{2} - a^{2} + 2 a - 1 - a^{3} + 2 a^{2} - a}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Add $- a^{2}$ and $2 a^{2}$ .

$\frac{a^{3} - a^{2} + a^{2} + 2 a - 1 - a^{3} - a}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Subtract $a$ from $2 a$ .

$\frac{a^{3} - a^{2} + a^{2} + a - 1 - a^{3}}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Subtract $a^{3}$ from $a^{3}$ .

$\frac{- a^{2} + a^{2} + a - 1 + 0}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Add $- a^{2} + a^{2} + a - 1$ and $0$ .

$\frac{- a^{2} + a^{2} + a - 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Add $- a^{2}$ and $a^{2}$ .

$\frac{0 + a - 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Add $0$ and $a$ .

$\frac{a - 1}{(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})}$

Step 5

Simplify the denominator.

Factor $1 + a$ out of $(1 + a) a^{2} + (a - 1) (- {(1 + a)}^{2})$ .

Factor $1 + a$ out of $(1 + a) a^{2}$ .

$\frac{a - 1}{(1 + a) (a^{2}) + (a - 1) (- {(1 + a)}^{2})}$

Factor $1 + a$ out of $(a - 1) (- {(1 + a)}^{2})$ .

$\frac{a - 1}{(1 + a) (a^{2}) + (1 + a) ((a - 1) (- (1 + a)))}$

Factor $1 + a$ out of $(1 + a) (a^{2}) + (1 + a) ((a - 1) (- (1 + a)))$ .

$\frac{a - 1}{(1 + a) (a^{2} + (a - 1) (- (1 + a)))}$

Apply the distributive property.

$\frac{a - 1}{(1 + a) (a^{2} + (a - 1) (- 1 \cdot 1 - a))}$

Multiply $- 1$ by $1$ .

$\frac{a - 1}{(1 + a) (a^{2} + (a - 1) (- 1 - a))}$

Expand $(a - 1) (- 1 - a)$ using the FOIL Method.

Apply the distributive property.

$\frac{a - 1}{(1 + a) (a^{2} + a (- 1 - a) - 1 (- 1 - a))}$

Apply the distributive property.

$\frac{a - 1}{(1 + a) (a^{2} + a \cdot - 1 + a (- a) - 1 (- 1 - a))}$

Apply the distributive property.

$\frac{a - 1}{(1 + a) (a^{2} + a \cdot - 1 + a (- a) - 1 \cdot - 1 - 1 (- a))}$

Simplify and combine like terms.

Simplify each term.

Move $- 1$ to the left of $a$ .

$\frac{a - 1}{(1 + a) (a^{2} - 1 \cdot a + a (- a) - 1 \cdot - 1 - 1 (- a))}$

Rewrite $- 1 a$ as $- a$ .

$\frac{a - 1}{(1 + a) (a^{2} - a + a (- a) - 1 \cdot - 1 - 1 (- a))}$

Rewrite using the commutative property of multiplication.

$\frac{a - 1}{(1 + a) (a^{2} - a - a \cdot a - 1 \cdot - 1 - 1 (- a))}$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$\frac{a - 1}{(1 + a) (a^{2} - a - (a \cdot a) - 1 \cdot - 1 - 1 (- a))}$

Multiply $a$ by $a$ .

$\frac{a - 1}{(1 + a) (a^{2} - a - a^{2} - 1 \cdot - 1 - 1 (- a))}$

Multiply $- 1$ by $- 1$ .

$\frac{a - 1}{(1 + a) (a^{2} - a - a^{2} + 1 - 1 (- a))}$

Multiply $- 1 (- a)$ .

Multiply $- 1$ by $- 1$ .

$\frac{a - 1}{(1 + a) (a^{2} - a - a^{2} + 1 + 1 a)}$

Multiply $a$ by $1$ .

$\frac{a - 1}{(1 + a) (a^{2} - a - a^{2} + 1 + a)}$

Add $- a$ and $a$ .

$\frac{a - 1}{(1 + a) (a^{2} - a^{2} + 1 + 0)}$

Add $- a^{2}$ and $0$ .

$\frac{a - 1}{(1 + a) (a^{2} - a^{2} + 1)}$

Subtract $a^{2}$ from $a^{2}$ .

$\frac{a - 1}{(1 + a) (0 + 1)}$

Add $0$ and $1$ .

$\frac{a - 1}{(1 + a) \cdot 1}$

Step 6

Multiply $1 + a$ by $1$ .

$\frac{a - 1}{1 + a}$

Simplify (a/(1+a)+(1-a)/a)/(a/(a-1)-(1+a)/a)

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