How do you solve 4/(x+2 )*( x^2-4)/(4x-8)4x+2⋅x2−44x−8?

1 Answer
Don't Memorise
Oct 19, 2015

4/(x+2 )*( x^2-4)/(4x-8) = color(green)(14x+2⋅x2−44x−8=1

Explanation:

4/(x+2 )*( x^2-4)/(4x-8) = 4/(x+2) X (x^2-2^2)/(4(x-2))4x+2⋅x2−44x−8=4x+2Xx2−224(x−2)

We know that color(blue)(a^2 - b^2 = (a+b)(a-b)a2−b2=(a+b)(a−b)

Hence x^2 - 2^2 = (x + 2)(x - 2)x2−22=(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

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