Simplify the rational expression. (Assume the denominator is nonzero.)
-$\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }$

A) $\frac { 3 ( x + 5 ) } { 4 ( x + 3 ) }$

B) $\frac { 9 } { 10 }$

C) $\frac { 3 ( x - 5 ) } { 4 ( x - 3 ) }$

D) $\frac { 5 } { 4 }$

Question

Simplify the rational expression. (Assume the denominator is nonzero.)
-$\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }$

A) $\frac { 3 ( x + 5 ) } { 4 ( x + 3 ) }$

B) $\frac { 9 } { 10 }$

C) $\frac { 3 ( x - 5 ) } { 4 ( x - 3 ) }$

D) $\frac { 5 } { 4 }$

Quizplus · Accepted Answer

First, factor both the numerator and the denominator. The numerator $9x^2 - 99x + 270$ can be factored as $9(x^2 - 11x + 30)$, which further factors into $9(x - 5)(x - 6)$. The denominator $12x^2 - 108x + 216$ can be factored as $12(x^2 - 9x + 18)$, which further factors into $12(x - 3)(x - 6)$. After canceling the common factor $(x - 6)$, the simplified expression is $\frac{9(x - 5)}{12(x - 3)}$, which simplifies to $\frac{3(x - 5)}{4(x - 3)}$.

Simplify the Rational Expression 9x2−99x+27012x2−108x+216\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }12x2−108x+2169x2−99x+270​

Simplify the Rational Expression $\frac { 9 x ^ { 2 } - 99 x + 270 } { 12 x ^ { 2 } - 108 x + 216 }$