Simplify the complex fraction. $$\frac { - \frac { 2 } { x } - \frac { 4 } { x + 2 } } { \frac { 7 } { x ^ { 2 } + 2 x } + \frac { 7 } { x } }$$
A) $- \frac { 2 ( 3 x + 2 ) } { 7 ( x + 3 ) }$
B) $- \frac { 7 ( 3 x - 2 ) } { 2 ( x + 3 ) }$
C) $- \frac { x + 2 } { 7 ( x + 3 ) }$
D) $- \frac { 2 ( 3 x - 2 ) } { 7 ( x + 3 ) }$
E) $- \frac { 3 x - 2 } { 2 ( x + 3 ) }$

Question

Quizplus · Accepted Answer

The correct answer is A because the numerator of the complex fraction is $- \frac { 2 } { x } - \frac { 4 } { x + 2 } = \frac { - 2 ( x + 2 ) - 4 x } { x ( x + 2 ) } = \frac { - 2 x - 4 - 4 x } { x ( x + 2 ) } = \frac { - 6 x - 4 } { x ( x + 2 ) }$ and the denominator of the complex fraction is $\frac { 7 } { x ^ { 2 } + 2 x } + \frac { 7 } { x } = \frac { 7 x + 7 ( x ^ { 2 } + 2 x ) } { x ( x ^ { 2 } + 2 x ) } = \frac { 7 x + 7 x ^ { 2 } + 14 x } { x ( x ^ { 2 } + 2 x ) } = \frac { 7 x ^ { 2 } + 21 x } { x ( x ^ { 2 } + 2 x ) }$. So the complex fraction is $\frac { - \frac { 2 } { x } - \frac { 4 } { x + 2 } } { \frac { 7 } { x ^ { 2 } + 2 x } + \frac { 7 } { x } } = \frac { - 6 x - 4 } { x ( x + 2 ) } \div \frac { 7 x ^ { 2 } + 21 x } { x ( x ^ { 2 } + 2 x ) } = \frac { - 6 x - 4 } { x ( x + 2 ) } \cdot \frac { x ( x ^ { 2 } + 2 x ) } { 7 x ^ { 2 } + 21 x } = \frac { - 6 x - 4 } { 7 x ^ { 2 } + 21 x }$.

Simplify the Complex Fraction −2x−4x+27x2+2x+7x\frac { - \frac { 2 } { x } - \frac { 4 } { x + 2 } } { \frac { 7 } { x ^ { 2 } + 2 x } + \frac { 7 } { x } }x2+2x7​+x7​−x2​−x+24​​

Simplify the Complex Fraction $\frac { - \frac { 2 } { x } - \frac { 4 } { x + 2 } } { \frac { 7 } { x ^ { 2 } + 2 x } + \frac { 7 } { x } }$