Simplify the fraction. $$\frac { x y + 6 x + 9 y + 54 } { x ^ { 3 } + 729 }$$ Assume that denominator is not 0 .
A) $\frac { y - 6 } { x ^ { 2 } - 9 x - 81 }$
B) $\frac { y + 9 } { x ^ { 2 } - 9 x + 81 }$
C) $\quad \frac { y + 6 } { x ^ { 2 } - 9 x + 81 }$
D) $\frac { y - 6 } { x ^ { 2 } - 9 x + 81 }$

Question

Quizplus · Accepted Answer

We can factor the numerator by taking out the common factors of $x$ and $9$: \begin{align*}
xy + 6x + 9y + 54 &= x(y+6) +9(y+6) \
&=(x+9)(y+6).
\end{align*} Therefore, the given expression simplifies to $\frac{(x+9)(y+6)}{x^3+729}$. We can factor $x^3+729$ using the sum of cubes formula as $(x+9)(x^2-9x+81)$. This gives the final simplified form of $\frac{y+6}{x^2-9x+81}$. Therefore, the answer is choice $\boxed{	extbf{(C)}}$.

Simplify the Fraction xy+6x+9y+54x3+729\frac { x y + 6 x + 9 y + 54 } { x ^ { 3 } + 729 }x3+729xy+6x+9y+54​

Simplify the Fraction $\frac { x y + 6 x + 9 y + 54 } { x ^ { 3 } + 729 }$