Simplify.
-$\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }$
A) $\frac { 49 } { x + 7 }$
B) $\frac { x + 7 } { 49 }$
C) $\frac { x - 7 } { 49 }$
D) $\frac { 49 } { x - 7 }$

Question

Quizplus · Accepted Answer

To simplify the expression, first find a common denominator for the numerator and the denominator. The numerator becomes $\frac{x^2 - 49}{49x}$ and the denominator becomes $\frac{x + 7}{x}$. Simplifying the fraction $\frac{\frac{x^2 - 49}{49x}}{\frac{x + 7}{x}}$ gives $\frac{x^2 - 49}{49(x + 7)}$. Recognizing $x^2 - 49$ as a difference of squares, it factors to $(x - 7)(x + 7)$. Canceling the common factor $(x + 7)$ from the numerator and denominator results in $\frac{x - 7}{49}$.

Simplify - x49−1x1+7x\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }1+x7​49x​−x1​​

Simplify
- $\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }$