Question

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}`?

Answer 1

`((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-1))/((x+2)(x+2)))`

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

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

And there you have your final answer!