Simplify the complex fraction.
-$$\frac { \frac { 4 } { 9 r - 1 } - 4 } { \frac { 4 } { 9 r - 1 } + 4 }$$
A) $\frac { 9 r } { 2 - 9 r }$
B) $\frac { 2 + 9 r } { 9 r }$
C) $\frac { 2 - r } { r }$
D) $\frac { 2 - 9 r } { 9 r }$

Question

Quizplus · Accepted Answer

To simplify the given complex fraction, we first find a common denominator for the numerators and denominators inside the larger fraction, which is $9r - 1$. We rewrite the fraction as:$$\frac{\frac{4}{9r-1} - \frac{4(9r-1)}{9r-1}}{\frac{4}{9r-1} + \frac{4(9r-1)}{9r-1}}$$Simplifying inside the numerators and denominators gives:$$\frac{\frac{4 - 4(9r-1)}{9r-1}}{\frac{4 + 4(9r-1)}{9r-1}}$$Further simplification:$$\frac{\frac{4 - 36r + 4}{9r-1}}{\frac{4 + 36r - 4}{9r-1}}$$Simplifying the numerators:$$\frac{\frac{-36r + 8}{9r-1}}{\frac{36r}{9r-1}}$$Since the denominators are the same, we can simplify the complex fraction by dividing the numerators:$$\frac{-36r + 8}{36r}$$Factoring out 4 from the numerator:$$\frac{4(2 - 9r)}{36r}$$Simplifying the fraction by dividing both the numerator and the denominator by 4:$$\frac{2 - 9r}{9r}$$Therefore, the simplified form of the given complex fraction is $\frac{2 - 9r}{9r}$, which corresponds to choice D.

Simplify the Complex Fraction 49r−1−449r−1+4\frac { \frac { 4 } { 9 r - 1 } - 4 } { \frac { 4 } { 9 r - 1 } + 4 }9r−14​+49r−14​−4​

Simplify the Complex Fraction $\frac { \frac { 4 } { 9 r - 1 } - 4 } { \frac { 4 } { 9 r - 1 } + 4 }$