Question

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

Answer 1

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)}`