Question

which of the following is the product of the rational expression shown below? make sure your answer is in reduced form x+1/x-4 * 5/x+1

Answer 1

5x/(x-4)

Explanation:

To multiply fractions, all we have to do is multiply the numerators together and the denominators together. If we do that, we get the following:

`(x+1)/(x-4)*(5x)/(x+1)=((x+1)(5x))/((x-4)(x+1))`

We notice that both the numerator and the denominator have an (x+1) term. Whenever you have something divided by itself, you get 1. In other words, they cancel out. As such, we can remove them from our answer to simplify it:

`(5x)/(x-4)`

If we do that, we get the expression above. 5x/(x-4) is the reduced product of the rational expression given.

Answer 2

C

Explanation:

`(x+1)/(x-4)` ×
`(5x)/(x+1)` ← cancel x + 1 on numerator and denominator

=
`(1)/(x-4)` ×
`(5x)/(1)`

=
`(5x)/(x-4)`