Precalculus Examples

$e^{\ln (\frac{1}{(1 - x) (1 + x)})}$

Step 1

Rewrite $\ln (\frac{1}{(1 - x) (1 + x)})$ as $\ln (1) - \ln ((1 - x) (1 + x))$ .

$e^{\ln (1) - \ln ((1 - x) (1 + x))}$

Step 2

The natural logarithm of $1$ is $0$ .

$e^{0 - \ln ((1 - x) (1 + x))}$

Step 3

Subtract $\ln ((1 - x) (1 + x))$ from $0$ .

$e^{- \ln ((1 - x) (1 + x))}$

Step 4

Rewrite $\ln ((1 - x) (1 + x))$ as $\ln (1 - x) + \ln (1 + x)$ .

$e^{- (\ln (1 - x) + \ln (1 + x))}$

Step 5

Apply the distributive property.

$e^{- \ln (1 - x) - \ln (1 + x)}$