Perform the indicated operations and express your answer in simplest form. $x - \frac { x ^ { 2 } } { x - 3 } + \frac { 3 } { x ^ { 2 } - 9 }$
A) $\frac { 3 x ^ { 2 } + 3 x + 3 } { x ^ { 2 } - 9 }$
B) $\frac { - 3 x ^ { 2 } - 9 x + 3 } { ( x + 3 ) ( x - 3 ) }$
C) $\frac { - 3 x ^ { 4 } - 9 x ^ { 2 } + 3 } { x ^ { 3 } + 3 x ^ { 3 } - 3 x - 27 }$
D) $\frac { 3 x ^ { 2 } + 9 x + 3 } { ( x + 3 ) ( x - 3 ) }$
E) $\frac { - 3 x ^ { 4 } - 9 x ^ { 2 } + 3 } { ( x + 3 ) \left( x ^ { 2 } - 9 \right) }$

Question

Quizplus · Accepted Answer

To simplify the expression, first find a common denominator, which is $x^2 - 9$ or equivalently $(x + 3)(x - 3)$. Rewrite each term with this common denominator: $x = \frac{x(x^2 - 9)}{x^2 - 9}$, $-\frac{x^2}{x-3} = -\frac{x^2(x+3)}{x^2 - 9}$, and $\frac{3}{x^2 - 9}$. Combine these fractions: $\frac{x(x^2 - 9) - x^2(x+3) + 3}{x^2 - 9}$. Simplify the numerator to get $\frac{-3x^2 - 9x + 3}{(x + 3)(x - 3)}$, which matches choice B.

Perform the Indicated Operations and Express Your Answer in Simplest x−x2x−3+3x2−9x - \frac { x ^ { 2 } } { x - 3 } + \frac { 3 } { x ^ { 2 } - 9 }x−x−3x2​+x2−93​

Perform the Indicated Operations and Express Your Answer in Simplest $x - \frac { x ^ { 2 } } { x - 3 } + \frac { 3 } { x ^ { 2 } - 9 }$