For this case we must factor.
Numerator:
[tex]2x ^ 2 + 13x + 20[/tex]
We must change the term of the medium by the sum of two numbers that when multiplied give as result [tex](2) (20) = 40[/tex], and when summed give as result +13.
These numbers are: 5 and 8
[tex](5) (8) = 40\\5 + 8 = 13[/tex]
So:
[tex]2x ^ 2 + 8x + 5x + 20[/tex]
We take common factor on both sides:
[tex]2x (x + 4) +5 (x + 4)\\(2x + 5) (x + 4)[/tex]
So, [tex]2x ^ 2 + 13x + 20 = (2x + 5) (x + 4)[/tex]
Denominator:
[tex]x ^ 2-5x-36[/tex]
We should look for two numbers that multiplied give -36 and added as a result -5.
-9 and +4
Thus, [tex]x ^ 2-5x-36 = (x-9) (x + 4)[/tex]
Then, [tex]\frac {2x ^ 2 + 13x + 20} {x ^ 2-5x-36} =[/tex]
[tex]\frac {(2x + 5) (x + 4)} {(x-9) (x + 4)} =\\\frac {(2x + 5)} {(x-9)} =[/tex]
Answer:
[tex]\frac {(2x + 5)} {(x-9)}[/tex]
