Multiply and simplify.
-$\frac { 90 x y ^ { 2 } } { x ^ { 2 n } - 36 } \cdot \frac { 10 x ^ { n } - 60 } { 9 x ^ { 2 } y ^ { 2 } }$
A) $\frac { 54 } { x \left( x ^ { n } + 6 \right) }$
B) $\frac { 10 } { x \left( x ^ { n } + 6 \right) }$
C) $\frac { 100 } { x \left( x ^ { n } + 6 \right) }$
D) $\frac { 100 x } { x ^ { n } + 6 }$

Question

Quizplus · Accepted Answer

First, factor the denominator of the first fraction and simplify the expression: $\frac{90xy^2}{x^{2n}-36} \cdot \frac{10x^n-60}{9x^2y^2} = \frac{90xy^2}{(x^n-6)(x^n+6)} \cdot \frac{10(x^n-6)}{9x^2y^2}$. Canceling common terms and simplifying gives $\frac{100}{x(x^n+6)}$.

Multiply and Simplify 90xy2x2n−36⋅10xn−609x2y2\frac { 90 x y ^ { 2 } } { x ^ { 2 n } - 36 } \cdot \frac { 10 x ^ { n } - 60 } { 9 x ^ { 2 } y ^ { 2 } }x2n−3690xy2​⋅9x2y210xn−60​

Multiply and Simplify $\frac { 90 x y ^ { 2 } } { x ^ { 2 n } - 36 } \cdot \frac { 10 x ^ { n } - 60 } { 9 x ^ { 2 } y ^ { 2 } }$