Subtract. $$\frac { x } { x + 3 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 9 }$$
A) $\frac { x ^ { 3 } + 3 x - 3 } { \left( x ^ { 2 } - 9 \right) ( x + 3 ) }$
B) $\frac { - 3 x - 3 } { x ^ { 2 } - 9 }$
C) $\frac { 2 x ^ { 2 } - 3 x - 3 } { x ^ { 2 } - 9 }$
D) $\frac { x ^ { 2 } + x - 3 } { - x ^ { 2 } + x + 12 }$

Question

Quizplus · Accepted Answer

To subtract the fractions, find a common denominator. The denominator $x^2 - 9$ can be factored into $(x + 3)(x - 3)$. The first fraction is missing the factor $x - 3$, so multiply the numerator and denominator of the first fraction by $x - 3$. This gives $\frac{x(x - 3)}{(x + 3)(x - 3)} - \frac{3 - x^2}{(x + 3)(x - 3)}$. Simplifying the numerators and combining the fractions, we get $\frac{x^2 - 3x - 3 + x^2}{x^2 - 9}$, which simplifies to $\frac{2x^2 - 3x - 3}{x^2 - 9}$.

Subtract xx+3−3−x2x2−9\frac { x } { x + 3 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 9 }x+3x​−x2−93−x2​

Subtract $\frac { x } { x + 3 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 9 }$