Question

Use the information below to complete the problem: p(x) = (1)/(x + 1)

Answer 1

Given:

The functions are:

$p(x)=\dfrac{1}{x+1}$

$q(x)=\dfrac{1}{x-1}$

To find:

The rational expression for $p(x)-q(x)$.

Solution:

We have,

$p(x)=\dfrac{1}{x+1}$

$q(x)=\dfrac{1}{x-1}$

Now,

$p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}$

$p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}$

$p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}$             $[\because a^2-b^2=(a-b)(a+b)]$

$p(x)-q(x)=\dfrac{-2}{x^2-1}$

Therefore, the required rational expression for $p(x)-q(x)$ is $\dfrac{-2}{x^2-1}$.