Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$\frac { 25 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 125 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 625 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$
A) $\frac { 1 + 5 x ^ { 3 } - 15 x } { 25 }$
B) $\frac { 1 - 5 x ^ { 3 } - 15 x } { 125 }$
C) $\frac { 1 + 5 x ^ { 3 } + 15 x } { 25 }$
D) $\frac { 1 - 5 x ^ { 3 } + 15 x } { 125 }$

Question

Quizplus · Accepted Answer

The numerator can be factored as $25(x^2-3)^3(1+5x)$. The denominator can be factored as $625(x^2-3)^3$. Dividing the numerator by the denominator gives $\frac{1+5x}{25}$.

Simplify the Rational Expression 25(x2−3)3+125x(x2−3)4625(x2−3)3\frac { 25 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 125 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 625 \left( x ^ { 2 } - 3 \right) ^ { 3 } }625(x2−3)325(x2−3)3+125x(x2−3)4​

Simplify the Rational Expression $\frac { 25 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 125 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 625 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$