Question

Simplify completely and find the restrictions on the variable.

Answer 1

\[\frac{ 12x+36 }{ x^2-4x-21 }\]

Answer 2

Factor!

Answer 3

how?!!?? help mehh

Answer 4

Factor out a 12 from the top.

Answer 5

For the bottom, it is a quadratic with leading coefficient 1, so find factors of -21 that add to make -4.

Answer 6

First start off with the denominator (bottom equation). We have to spread it apart. So, it would be (x-7) (x+3). Now, how I got that was I took the number 21 (the last number) and broke it down, so 7 and 3 both go into it, 7x3=21. We have two x's so one for each of the numbers. Than you have to find out which one will be negative and which one will be positive. If I take (x-7) (x+3) and distribute them, I should get x^2-4x-21, and I do. In which (x-7) (x+3) is right. Than for numerator, 12x+36, what's common in those two numbers? In other words, what can I take out of both of them? I can take out a 12, so I would be left with 12(x+3). If I distribute the 12 back in there I should get 12x+36, and I do, which means it's right. Finally how I solve this is I have 12(x+3) over (x-7) (x+3). Do you see how you have a x+3 on the top and the bottom equation? That's what you want! You want to be able to cancel them out. So I would cancel the x+3 from the top and the bottom, and I will be left with 12 over x-7. Hopefully that makes sense, but it's a long process because you have to break the equations down.

Answer 7

@xxmileyxxd , perhaps you can explain how to use that to find the restricted domain.