Question

walk me through this problem: 5x+30/x+4 x x+4/x^2+12x+36

Answer 1

Multiplying fractions?

Answer 2

I would suppose

Answer 3

Let's start by writing it out so we can see more clearly:
\[\LARGE \frac{5x+30}{x+4}*\frac{x+4}{x^2+12x+36}\]

Answer 4

First step, factor what you can.

Answer 5

factor x+4??

Answer 6

Well it's already factored, so move on to what you can factor. Try the 5x+30 and x^2+12x+36

Answer 7

you can factor the 5 through 5x+30?

Answer 8

Yup, so what do you get?

Answer 9

x+6

Answer 10

\[\LARGE \frac{5(x+6)}{x+4}*\frac{x+4}{x^2+12x+36}\]
Yup, now move on to the next

Answer 11

factor the 12 through x^2+12x+36 and get x^2+x+3?

Answer 12

If there was a 12 infront of the x^2 it would work, but not in this case.

Answer 13

then idk :l

Answer 14

Well, what adds up to 12 and multiplies to 36?

Answer 15

Factor 36.

Answer 16

6

Answer 17

Right! So it would just be (x+6)(x+6) or the easier way to write it is (x+6)^2.
\[\LARGE \frac{5(x+6)}{x+4}*\frac{x+4}{(x+6)^2}\]
Now that we've factored, we can cross cancel anything that's the same. So notice anything that's the same?

Answer 18

(x+6) and x+4

Answer 19

Yup, they cancel and we are left with:
\[\LARGE \frac{5}{1}*\frac{1}{(x+6)}\]

Now just multiply that :)

Answer 20

which would be 5x+30?

Answer 21

If it was \[\LARGE \frac{1}{5}*\frac{1}{x+6}\] then yes, but not in this case.
We multiply across, so:
\[\LARGE \frac{5*1}{1*(x+6)}=\frac{5}{x+6}\]

Answer 22

Two completely different answers, so be careful.

Answer 23

ahh thank you

Answer 24

Anytime :)