Question

How do you solve `(x-4) / (x+2) + 2 /( x-2) = 17 / (x^2-4)`?

Answer 1

`x=-1` or `x=5`

Explanation:

Start from the left hand side:

`(x-4)/(x+2)+2/(x-2)=((x-4)(x-2)+2(x+2))/((x+2)(x-2))=(x^2-6x+8 +2x+4)/(x^2-4)=(x^2-4x+12)/(x^2-4)`

which is equal to the right hand side `17/(x^2-4)`.

So we have
`x^2-4x+12=17`
`x^2-4x-5=0`
`(x+1)(x-5)=0`
`x=-1` or `x=5`