Simplify the complex fraction using Method 2.
-$\frac { \frac { 6 } { 9 r - 1 } - 6 } { \frac { 6 } { 9 r - 1 } + 6 }$
A) $\frac { 2 + 9 r } { 9 r }$
B) $\frac { 2 - r } { r }$
C) $\frac { 2 - 9 r } { 9 r }$
D) $\frac { 9 r } { 2 - 9 r }$

Question

Quizplus · Accepted Answer

To simplify the given complex fraction, we first find a common denominator for the numerators and denominators within the complex fraction, which is $9r - 1$. We then rewrite the fraction as:$$\frac{\frac{6}{9r-1} - \frac{6(9r-1)}{9r-1}}{\frac{6}{9r-1} + \frac{6(9r-1)}{9r-1}}$$Simplifying within the numerators and denominators gives:$$\frac{\frac{6 - 6(9r-1)}{9r-1}}{\frac{6 + 6(9r-1)}{9r-1}}$$Further simplification yields:$$\frac{\frac{6 - 54r + 6}{9r-1}}{\frac{6 + 54r - 6}{9r-1}}$$Simplifying the numerators:$$\frac{\frac{-54r + 12}{9r-1}}{\frac{54r}{9r-1}}$$Dividing the numerators and denominators by their common term:$$\frac{-54r + 12}{54r}$$Factoring out a 6 from the numerator:$$\frac{6(-9r + 2)}{54r}$$Simplifying the fraction by dividing both the numerator and the denominator by 6:$$\frac{-9r + 2}{9r}$$Rearranging the numerator:$$\frac{2 - 9r}{9r}$$Therefore, the simplified form of the given complex fraction is $\frac{2 - 9r}{9r}$, which matches choice C.

Simplify the Complex Fraction Using Method 2 69r−1−669r−1+6\frac { \frac { 6 } { 9 r - 1 } - 6 } { \frac { 6 } { 9 r - 1 } + 6 }9r−16​+69r−16​−6​

Simplify the Complex Fraction Using Method 2 $\frac { \frac { 6 } { 9 r - 1 } - 6 } { \frac { 6 } { 9 r - 1 } + 6 }$