Perform the indicated operation. Simplify if possible.
-$$\left( \frac { x } { x + 3 } - \frac { x } { x - 3 } \right) \div \frac { x } { 7 x + 21 }$$
A) 0
B) $- \frac { 42 } { ( x - 3 ) }$
C) 14
D) $- \frac { 6 x ^ { 2 } } { 7 ( x + 3 ) ^ { 2 } ( x - 3 ) }$

Question

Quizplus · Accepted Answer

The correct answer is B because $$\left( \frac { x } { x + 3 } - \frac { x } { x - 3 } \right) \div \frac { x } { 7 x + 21 }$$$$= \frac { x ( x - 3 ) - x ( x + 3 ) } { ( x + 3 ) ( x - 3 ) } \cdot \frac { 7 x + 21 } { x }$$$$= \frac { x ^ { 2 } - 3 x - x ^ { 2 } - 3 x } { x + 3 } \cdot \frac { 7 x + 21 } { x }$$$$= \frac { - 6 x } { x + 3 } \cdot \frac { 7 x + 21 } { x }$$$$= \frac { - 6 ( 7 x + 21 ) } { x ( x + 3 ) }$$$$= \frac { - 42 } { x - 3 }$$

Perform the Indicated Operation (xx+3−xx−3)÷x7x+21\left( \frac { x } { x + 3 } - \frac { x } { x - 3 } \right) \div \frac { x } { 7 x + 21 }(x+3x​−x−3x​)÷7x+21x​

Perform the Indicated Operation $\left( \frac { x } { x + 3 } - \frac { x } { x - 3 } \right) \div \frac { x } { 7 x + 21 }$