Verified Answer :

rarrininger

x^2+7x+12/x^2-x-12
x^2+4x+3x+12/x^2+3x-4x-12
x (x+4) +3(x+4)/ x (x+3)-4(x+3)
(x+3)(x+4)/(x-4)(x+3)

x+4/x-4

Answer:

\(\frac{(x+4)}{(x-4)}\)

Step-by-step explanation:

Given : \(\frac{x^2+7x+12}{x^2-x-12}\)

Solution:

\(\frac{x^2+7x+12}{x^2-x-12}\)

Factorize the numerator and denominator.

\(\frac{x^2+3x+4x+12}{x^2-4x+3x-12}\)

\(\frac{x(x+3)+4(x+3)}{x(x-4)+3(x-4)}\)

\(\frac{(x+4)(x+3)}{(x-4)(x+3)}\)

\(\frac{(x+4)}{(x-4)}\)

So, \(\frac{x^2+7x+12}{x^2-x-12}\) =  \(\frac{(x+4)}{(x-4)}\)

Hence Option B is correct.

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