Question

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

and q(x) = (1)/(x - 1)
Perform the operation and show that it results in another rational expression.

p(x) - q(x)

Answer 1

Given:

The functions are:

`p(x)=(1)/(x+1)`

`q(x)=(1)/(x-1)`

To find:

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

Solution:

We have,

`p(x)=(1)/(x+1)`

`q(x)=(1)/(x-1)`

Now,

`p(x)-q(x)=(1)/(x+1)-(1)/(x-1)`

`p(x)-q(x)=((x-1)-(x+1))/((x+1)(x-1))`

`p(x)-q(x)=(x-1-x-1)/(x^2-1^2)`
`[\because a^2-b^2=(a-b)(a+b)]`

`p(x)-q(x)=(-2)/(x^2-1)`

Therefore, the required rational expression for
`p(x)-q(x)` is
`(-2)/(x^2-1)`.