Perform the indicated operation and express your answer in simplest form. $\frac { 7 x } { x ^ { 2 } + 2 x } + \frac { 8 } { x }$
A) $\frac { 15 x + 16 } { x + 2 }$
B) $\frac { 15 x + 16 } { x ( x + 2 ) }$
C) $\frac { 7 x + 16 } { x ( x + 2 ) }$

Question

Quizplus · Accepted Answer

To add these two fractions, we need a common denominator. The first fraction already has a denominator of $x(x+2)$, so we just need to adjust the second fraction to have the same denominator: $$\frac{7x}{x^2+2x}+\frac{8}{x} = \frac{7x}{x^2+2x}+\frac{8}{x}\cdot\frac{x+2}{x+2}=\frac{7x}{x^2+2x}+\frac{8x+16}{x(x+2)}.$$ Combining the fractions gives us $$\frac{7x+8x+16}{x(x+2)} = \boxed{	extbf{(B)}\ \frac{15x+16}{x(x+2)}}.$$

Perform the Indicated Operation and Express Your Answer in Simplest 7xx2+2x+8x\frac { 7 x } { x ^ { 2 } + 2 x } + \frac { 8 } { x }x2+2x7x​+x8​

Perform the Indicated Operation and Express Your Answer in Simplest $\frac { 7 x } { x ^ { 2 } + 2 x } + \frac { 8 } { x }$