Question

How do you solve `4/(x+2 )*( x^2-4)/(4x-8)`?

Answer 1

`4/(x+2 )*( x^2-4)/(4x-8) = color(green)(1`

Explanation:

`4/(x+2 )*( x^2-4)/(4x-8) = 4/(x+2) X (x^2-2^2)/(4(x-2))`

We know that `color(blue)(a^2 - b^2 = (a+b)(a-b)`

Hence `x^2 - 2^2 = (x + 2)(x - 2)`

The expression will equal

`cancel(4)/cancel((x+2)) X {cancel((x+2))cancel((x-2))}/(cancel(4)cancel((x-2)))`

`= 1`