Divide as indicated.
-$$\frac { x ^ { 2 } - 17 x + 66 } { 11 - x } \div ( x + 6 )$$
A) $- \frac { x - 6 } { x + 6 }$
B) $- 1$
C) $- ( x - 6 ) ( x + 6 )$
D) $- \frac { x + 6 } { x - 6 }$

Question

Quizplus · Accepted Answer

First, factor the numerator: $x^2 - 17x + 66 = (x - 6)(x - 11)$. The expression becomes $\frac{(x - 6)(x - 11)}{11 - x} \div (x + 6)$. Notice that $11 - x$ can be rewritten as $-(x - 11)$, which cancels out with the $(x - 11)$ in the numerator. Simplifying gives $-\frac{x - 6}{x + 6}$.

Divide as Indicated x2−17x+6611−x÷(x+6)\frac { x ^ { 2 } - 17 x + 66 } { 11 - x } \div ( x + 6 )11−xx2−17x+66​÷(x+6)

Divide as Indicated $\frac { x ^ { 2 } - 17 x + 66 } { 11 - x } \div ( x + 6 )$