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

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

Step 1

Multiply the numerator and denominator of the complex fraction by $a$ .

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $a$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $a$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Multiply $a$ by $1$ .

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

Step 5

Simplify the denominator.

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

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

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

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