Simplify (2/(1-a)+2/(1+a))/(2/(1+a)-2/(1-a))

$\frac{\frac{2}{1 - a} + \frac{2}{1 + a}}{\frac{2}{1 + a} - \frac{2}{1 - a}}$

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

Multiply $\frac{\frac{2}{1 - a} + \frac{2}{1 + a}}{\frac{2}{1 + a} - \frac{2}{1 - a}}$ by $\frac{(1 - a) (1 + a)}{(1 - a) (1 + a)}$ .

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $1 - a$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $1 + a$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $1 + a$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $1 - a$ .

Move the leading negative in $- \frac{2}{1 - a}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $(1 + a) \cdot 2 + (1 - a) \cdot 2$ and $(1 - a) \cdot 2 + (1 + a) \cdot - 2$ .

Factor $2$ out of $(1 + a) \cdot 2$ .

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

Factor $2$ out of $(1 - a) \cdot 2$ .

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

Factor $2$ out of $2 \cdot (1 + a) + 2 \cdot (1 - a)$ .

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

Cancel the common factors.

Factor $2$ out of $(1 - a) \cdot 2$ .

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

Factor $2$ out of $(1 + a) \cdot - 2$ .

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

Factor $2$ out of $2 \cdot (1 - a) + 2 ((1 + a) \cdot - 1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Add $1$ and $1$ .

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

Subtract $a$ from $a$ .

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

Add $0$ and $2$ .

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

Simplify the denominator.

Apply the distributive property.

$\frac{2}{1 - a + 1 \cdot - 1 + a \cdot - 1}$

Multiply $- 1$ by $1$ .

$\frac{2}{1 - a - 1 + a \cdot - 1}$

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

$\frac{2}{1 - a - 1 - 1 \cdot a}$

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

$\frac{2}{1 - a - 1 - a}$

Subtract $1$ from $1$ .

$\frac{2}{- a + 0 - a}$

Add $- a$ and $0$ .

$\frac{2}{- a - a}$

Subtract $a$ from $- a$ .

$\frac{2}{- 2 a}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ and $- 2$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $- 2 a$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{- a}$

Cancel the common factor of $1$ and $- 1$ .

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

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

Move the negative in front of the fraction.

$- \frac{1}{a}$

Simplify (2/(1-a)+2/(1+a))/(2/(1+a)-2/(1-a))

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