Question

How do you solve `(8(x-1))/(x^2-4)=4/(x-2)`?

Answer 1

`x=4`

Explanation:

Rewrite this as follows

`(8(x-1))/(x^2-4)=4/(x-2)`

`[8(x-1)]/[(x-2)(x+2)]-4/(x-2)=0`

`1/(x-2)*[(8(x-1))/(x+2)-4]=0`

`1/[(x-2)*(x+2)][8(x-1)-4(x+2)]=0`

`[8x-8-4x-8]/[(x-2)(x+2)]=0`

`(4(x-4))/[(x-2)(x+2)]=0`

From the last equation we get that `x=4`

Footnote

For the (initial) equation to hold must be `x!=2` and `x!=-2`