How do you multiply and simplify \frac {x^2 + 6x + 8} { x^2- 5x + 4} \cdot \frac { x ^ { 2} + 3x - 4} { x ^ { 2} + 4x + 4}x2+6x+8x2−5x+4⋅x2+3x−4x2+4x+4?

1 Answer
Elliott G.
Apr 27, 2018

((x+4)^2)/((x-4)(x+2))(x+4)2(x−4)(x+2)

Explanation:

Okay, so first things first: Factor.

You're going to want to factor the equations, from there, you can simplify. So, factor each numerator and denominator. You should get:

(((x+4)(x+2))/((x-4)(x-1)))((x+4)(x+2)(x−4)(x−1))*(((x+4)(x-1))/((x+2)(x+2)))((x+4)(x−1)(x+2)(x+2))

From here, you can see how terms cancel and combine. So, you can tell that one x+2x+2 will cancel and the x-1x−1's will cancel, and the x+4x+4's will combine into (x+4)^2(x+4)2.

Then you'll have:
((x+4)^2)/((x-4)(x+2))(x+4)2(x−4)(x+2)

And there you have your final answer!

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