Divide. Simplify if possible.
-$$( x + 2 ) \div \frac { x ^ { 2 } - 5 x + 6 } { 3 - x }$$
A) $- \frac { x + 2 } { x - 2 }$
B) $- 1$
C) - \frac { x - 2 } { x + 2 }\)
D) $- ( x - 2 ) ( x + 2 )$

Question

Quizplus · Accepted Answer

To divide by a fraction, you multiply by its reciprocal. So, $(x + 2) \div \frac{x^2 - 5x + 6}{3 - x}$ becomes $(x + 2) \times \frac{3 - x}{x^2 - 5x + 6}$. Factor $x^2 - 5x + 6$ into $(x - 2)(x - 3)$. The expression simplifies to $\frac{x + 2}{(x - 2)(x - 3)} \times \frac{3 - x}{1}$. Notice that $3 - x$ is $-(x - 3)$, so the expression simplifies further to $-\frac{x + 2}{x - 2}$, which matches choice A.

Divide Simplify If Possible (x+2)÷x2−5x+63−x( x + 2 ) \div \frac { x ^ { 2 } - 5 x + 6 } { 3 - x }(x+2)÷3−xx2−5x+6​

Divide Simplify If Possible $( x + 2 ) \div \frac { x ^ { 2 } - 5 x + 6 } { 3 - x }$