How does $\frac{x^2 + 6x + 5}{x^2 - x - 2}$ simplify to $\frac{(x + 5)(x + 1)}{(x - 2)(x + 1)}$?

Question

I stumbled upon following rational, where the right hand of equation is a simplification:

$$\frac{x^2 + 6x + 5}{x^2 - x - 2} = \frac{(x + 5)(x + 1)}{(x - 2)(x + 1)}$$

I can't understand how do you derive this simplification, what rules apply here?
Secondly, I want to search google for more (generic) information but I'm not even sure what should I search for?

EDIT:

Btw. this comes from this video link, but it doesn't explain my question.

Do you know how to factor quadratics? This is basically that. — Aiden Chow, Jun 05 '20 at 22:09
No I don't, but thank you for the term, now I know what courses I need to watch! — metablaster, Jun 05 '20 at 22:10
Look for something like "how to factor quadratic", you should find lots of resources. Typical methods are completing the square and findings the roots I guess. There are some resources on this site as well, although they seem to be specific, maybe look at Is there any method to factorize quadratic polynomial other than cross-method? and How to rearrange a quadratic into its factorized form?. — Sil, Jun 05 '20 at 22:21

score 1 · Accepted Answer · answered Jun 05 '20 at 22:16

1

1) Find the roots of the numerator. These are $-5, -1$, Find the roots of the denominator. These are $2, -1$.

2) Search for "roots of quadratic equations" or "factoring quadratic polynomials".

answered Jun 05 '20 at 22:16

markvs

1 Answers1