Divide.
-$\frac { a ^ { 2 } - 14 a + 45 } { 9 - a } \div ( a + 5 )$
A)-1
B) $- \frac { a - 5 } { a + 5 }$
C) $- ( a - 5 ) ( a + 5 )$
D) $- \frac { a + 5 } { a - 5 }$

Question

Quizplus · Accepted Answer

First, factor the numerator $a^2 - 14a + 45$ to $(a-9)(a-5)$. The expression becomes $\frac{(a-9)(a-5)}{9-a} \div (a+5)$. Notice that $9-a$ can be rewritten as $-(a-9)$, which cancels out with $(a-9)$ in the numerator, leaving $\frac{a-5}{-1} \div (a+5)$. Simplifying further gives $-\frac{a-5}{a+5}$, which matches choice B.

Divide - a2−14a+459−a÷(a+5)\frac { a ^ { 2 } - 14 a + 45 } { 9 - a } \div ( a + 5 )9−aa2−14a+45​÷(a+5)

Divide
- $\frac { a ^ { 2 } - 14 a + 45 } { 9 - a } \div ( a + 5 )$