Simplify the complex fraction.
-$$\frac { \frac { x } { 5 } - \frac { 3 } { x } } { \frac { 3 } { x } + \frac { 3 } { 5 } }$$
A) $\frac { x ^ { 2 } - 15 } { x + 15 }$
B) $\frac { x ^ { 2 } - 15 } { 3 x + 15 }$
C) $\frac { x ^ { 2 } - 15 } { 3 ( x + 5 ) }$
D) $\frac { x ^ { 2 } - 3 } { 3 x + 15 }$

Question

Quizplus · Accepted Answer

To simplify the complex fraction, we first need to find a common denominator for both numerator and denominator. The common denominator is 5x. Then we multiply the numerator and denominator by the common denominator to get rid of the fractions in the numerator and denominator.

$$\frac { \frac { x } { 5 } - \frac { 3 } { x } } { \frac { 3 } { x } + \frac { 3 } { 5 } }=\frac{\frac{x}{5}\cdot x-\frac{3}{x}\cdot5x}{\frac{3}{x}\cdot5x+\frac{3}{5}\cdot5x}=\frac{x^2-15}{3(x+5)}$$

Therefore, the simplified form of the complex fraction is $\frac { x ^ { 2 } - 15 } { 3 ( x + 5 ) }$. The correct answer choice is C.

Simplify the Complex Fraction x5−3x3x+35\frac { \frac { x } { 5 } - \frac { 3 } { x } } { \frac { 3 } { x } + \frac { 3 } { 5 } }x3​+53​5x​−x3​​

Simplify the Complex Fraction $\frac { \frac { x } { 5 } - \frac { 3 } { x } } { \frac { 3 } { x } + \frac { 3 } { 5 } }$