Question

How do you solve `\frac { 4} { x - 1} + \frac { 4} { x + 1} = 3`?

Answer 1

`x=3` and `x=(-1)/3`

Explanation:

First, we have to give the terms on the left a common denominator.
To do this, we will multiply `4/(x-1)` by `(x+1)/(x+1)` and `4/(x+1)` by `(x-1)/(x-1)`

Here is the result:

`(4x+4)/(xˆ2-1)+(4x-4)/(xˆ2-1)=3`

We will add the like terms together.

`(8x)/(xˆ2-1)=3`

Now, we multiply both sides by `xˆ2-1`

`8x=3xˆ2-3`

Since this is a quadratic, we'll set equal to zero and factor.

`3xˆ2-8x-3=0`

`(x-3)(3x+1)=0`

Setting each factor equal to 0, we get

`x=3` and `x=(-1)/3`

Neither solution is extraneous.