Answer:
[tex]\frac{(x+4)}{(x-4)}[/tex]
Step-by-step explanation:
Given : [tex]\frac{x^2+7x+12}{x^2-x-12}[/tex]
Solution:
[tex]\frac{x^2+7x+12}{x^2-x-12}[/tex]
Factorize the numerator and denominator.
[tex]\frac{x^2+3x+4x+12}{x^2-4x+3x-12}[/tex]
[tex]\frac{x(x+3)+4(x+3)}{x(x-4)+3(x-4)}[/tex]
[tex]\frac{(x+4)(x+3)}{(x-4)(x+3)}[/tex]
[tex]\frac{(x+4)}{(x-4)}[/tex]
So, [tex]\frac{x^2+7x+12}{x^2-x-12}[/tex] = [tex]\frac{(x+4)}{(x-4)}[/tex]
Hence Option B is correct.
