For that case, we factor the numerator and denominator:
Numerator:
[tex]2x ^ 2 + 7x + 3[/tex]
We rewrite the term of the medium as a sum of two terms whose product is:
[tex]2 * 3 = 6[/tex]
And the sum is:
+7
Those numbers are 6 and 1.
[tex]2x ^ 2 + 6x + 1x + 3[/tex]
We factor the maximum common denominator of each group:
[tex]2x (x + 3) +1 (x + 3)[/tex]
So:
[tex]2x ^ 2 + 7x + 3 = (2x + 1) (x + 3)[/tex]
Denominator:
[tex](x ^ 2-9) = (x + 3) (x-3)[/tex]
So, we have:
[tex]\frac {(2x + 1) (x + 3)} {(x + 3) (x-3)}[/tex]
Simplifying we have left:
[tex]\frac {(2x + 1)} {(x-3)}[/tex]
Answer:
Option A
