Simplify the complex fraction. $\frac { \left( \frac { x ^ { 2 } + 5 x - 36 } { x + 6 } \right) } { 3 x - 12 }$
A) $\frac { x + 9 } { 3 ( x + 6 ) } , x \neq 4$
B) $\frac { x - 9 } { 3 ( x + 6 ) } , x \neq - 4$
C) $\frac { x - 4 } { 3 ( x - 9 ) } , x \neq - 4$
D) $\frac { x + 6 } { 3 ( x - 4 ) } , x \neq 4$
E) $\frac { x + 4 } { 3 ( x + 9 ) } , x \neq 4$

Question

Quizplus · Accepted Answer

First, factor the numerator and denominator where possible. The numerator $\frac{x^2 + 5x - 36}{x + 6}$ simplifies to $\frac{(x + 9)(x - 4)}{x + 6}$ after factoring $x^2 + 5x - 36$. The denominator $3x - 12$ simplifies to $3(x - 4)$ after factoring out the 3. Thus, the complex fraction simplifies to $\frac{x + 9}{3(x + 6)}$, with the condition $x \neq 4$ to avoid division by zero in the original denominator.

Simplify the Complex Fraction (x2+5x−36x+6)3x−12\frac { \left( \frac { x ^ { 2 } + 5 x - 36 } { x + 6 } \right) } { 3 x - 12 }3x−12(x+6x2+5x−36​)​

Simplify the Complex Fraction $\frac { \left( \frac { x ^ { 2 } + 5 x - 36 } { x + 6 } \right) } { 3 x - 12 }$