Question

Simplify completely 2x2+13x+20/x2-5x-36

Answer 1

Here. I hope you can see it.

Answer 2

For this case we must factor.

Numerator:

$2x ^ 2 + 13x + 20$

We must change the term of the medium by the sum of two numbers that when multiplied give as result $(2) (20) = 40$, and when summed give as result +13.

These numbers are: 5 and 8

$(5) (8) = 40\\5 + 8 = 13$

So:

$2x ^ 2 + 8x + 5x + 20$

We take common factor on both sides:

$2x (x + 4) +5 (x + 4)\\(2x + 5) (x + 4)$

So, $2x ^ 2 + 13x + 20 = (2x + 5) (x + 4)$

Denominator:

$x ^ 2-5x-36$

We should look for two numbers that multiplied give -36 and added as a result -5.

-9 and +4

Thus, $x ^ 2-5x-36 = (x-9) (x + 4)$

Then, $\frac {2x ^ 2 + 13x + 20} {x ^ 2-5x-36} =$

$\frac {(2x + 5) (x + 4)} {(x-9) (x + 4)} =\\\frac {(2x + 5)} {(x-9)} =$

Answer:

$\frac {(2x + 5)} {(x-9)}$