What is the simplified form of (x-3)/(x^2+x-12) * (x+4)/(x^2 + 8x + 16)x−3x2+x−12⋅x+4x2+8x+16?

1 Answer
John D.
Jun 12, 2018

1/(x+4)^21(x+4)2

Explanation:

First, factor the fractions:

(x-3)/(x^2+x-12) * (x+4)/(x^2+8x+16)x−3x2+x−12⋅x+4x2+8x+16

(x-3)/((x-3)(x+4)) * (x+4)/((x+4)(x+4))x−3(x−3)(x+4)⋅x+4(x+4)(x+4)

Now, combine them:

((x-3)(x+4))/((x-3)(x+4)^3)(x−3)(x+4)(x−3)(x+4)3

(cancel((x-3))cancel((x+4)))/(cancel((x-3))(x+4)^(cancel3 color(white)"." color(red)2))

1/(x+4)^2

Or if you want to expand it back out:

1/(x^2+8x+16)

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