Question

What is the product of the rational expressions below?

x + 5/x + 7 * 10x / x - 7

Answer 1

So you have:
(x + 5)/(x + 7) * (10x)/(x - 7) correct?

Answer 2

yes

Answer 3

First things first, I would probably try to even out your denominator like you would with any ordinary fraction problem so, multiply the second fraction by '-1' first to even your denominators.
(x + 5)/(x + 7) * -1(10x)/-1(x - 7) ~ Which gives you:
(x + 5)/(x + 7) * -10x/-x + 7 ~ Hmmm... I thought that would work... hold on.

Answer 4

10x • (x + 5)
—————— but need this simplified
(x + 7) • (x - 7)

Answer 5

Oh... thanks that actually helps a lot. Okay:
10x(x + 5) = 10x^2 + 50x
--------- =
(x + 7)(x - 7) = x^2 - 49
Your final answer being:
10x^2 + 50x
-----------
x^2 - 49
I don't think you can simplify further, you do know how I got the (x+7)(x-7) to come out with x^2 - 49, right?