Divide. Simplify if possible.
-$$\frac { x ^ { 2 } - 12 x + 27 } { 3 - x } \div ( x + 9 )$$
A) $- 1$
B) $- \frac { x - 9 } { x + 9 }$
C) $- ( x - 9 ) ( x + 9 )$
D) $- \frac { x + 9 } { x - 9 }$

Question

Quizplus · Accepted Answer

First, factor the numerator: $x^2 - 12x + 27 = (x - 3)(x - 9)$. The division $\frac{x^2 - 12x + 27}{3 - x}$ simplifies to $\frac{(x - 3)(x - 9)}{3 - x}$. Since $3 - x = -(x - 3)$, this further simplifies to $- (x - 9)$. The entire expression becomes $- (x - 9) \div (x + 9)$, which simplifies to $- \frac{x - 9}{x + 9}$.

Divide Simplify If Possible x2−12x+273−x÷(x+9)\frac { x ^ { 2 } - 12 x + 27 } { 3 - x } \div ( x + 9 )3−xx2−12x+27​÷(x+9)

Divide Simplify If Possible $\frac { x ^ { 2 } - 12 x + 27 } { 3 - x } \div ( x + 9 )$