Simplify the rational expression.
-$$\frac { x ^ { 3 } - 5 x ^ { 2 } + 2 x - 10 } { 3 x ^ { 2 } - 75 }$$
A) $\frac { x ^ { 3 } + 2 x - 7 } { - 12 }$ (Provided $\left. x \neq - 5 \right)$
B) $\frac { x ^ { 2 } + 2 } { 3 x - 15 } \quad ($ Provided $x \neq - 5 )$
C) $\frac { x ^ { 2 } + 2 } { 3 ( x + 5 ) } \quad$ (Provided $\left. x \neq 5 \right)$
D) $\frac { x ^ { 3 } - 5 x ^ { 2 } + 2 x - 10 } { 3 x ^ { 2 } - 75 }$; cannot be simplified

Question

Quizplus · Accepted Answer

First, factor both the numerator and the denominator. The numerator can be factored by grouping: $x^3 - 5x^2 + 2x - 10 = x^2(x - 5) + 2(x - 5) = (x^2 + 2)(x - 5)$. The denominator can be factored as $3x^2 - 75 = 3(x^2 - 25) = 3(x + 5)(x - 5)$. Thus, the expression simplifies to $\frac{x^2 + 2}{3(x + 5)}$, provided $x \neq 5$ to avoid division by zero.

Simplify the Rational Expression x3−5x2+2x−103x2−75\frac { x ^ { 3 } - 5 x ^ { 2 } + 2 x - 10 } { 3 x ^ { 2 } - 75 }3x2−75x3−5x2+2x−10​

Simplify the Rational Expression $\frac { x ^ { 3 } - 5 x ^ { 2 } + 2 x - 10 } { 3 x ^ { 2 } - 75 }$