Simplify the rational expression. $$\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$$
A) $\frac { x ^ { 2 } + 2 } { 3 ( x + 4 ) } \quad ($ Provided $x \neq 4 )$
B) $\frac { x ^ { 3 } + 2 x - 6 } { - 9 }$ (Provided $\left. x \neq - 4 \right)$
C) $\frac { x ^ { 2 } + 2 } { 3 x - 12 }$ (Provided $x \neq - 4$ )
D) $\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$; cannot be simplified

Question

Quizplus · Accepted Answer

First, factor both the numerator and the denominator. The numerator can be factored by grouping, and the denominator is a difference of squares. After factoring, common factors can be canceled out, leading to the simplified expression in choice A.

Simplify the Rational Expression x3−4x2+2x−83x2−48\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }3x2−48x3−4x2+2x−8​

Simplify the Rational Expression $\frac { x ^ { 3 } - 4 x ^ { 2 } + 2 x - 8 } { 3 x ^ { 2 } - 48 }$