Simplify.
-$\frac { 1 - \frac { 5 } { x } } { x - \frac { 25 } { x } }$
A) $x + 5$
B) $\frac { 1 } { x + 5 }$
C) $x - 5$
D) $\frac { 1 } { x - 5 }$

Question

Quizplus · Accepted Answer

To simplify the given expression, first find a common denominator for the fractions within the numerator and the denominator. The common denominator is $x$, so rewrite the expression as $\frac { \frac { x - 5 } { x } } { \frac { x^2 - 25 } { x } }$. Simplify further by canceling out $x$ in the numerator and the denominator, which gives $\frac { x - 5 } { x^2 - 25 }$. Recognize that $x^2 - 25$ is a difference of squares, which factors into $(x + 5)(x - 5)$. Thus, the expression simplifies to $\frac { 1 } { x + 5 }$.

Simplify - 1−5xx−25x\frac { 1 - \frac { 5 } { x } } { x - \frac { 25 } { x } }x−x25​1−x5​​

Simplify
- $\frac { 1 - \frac { 5 } { x } } { x - \frac { 25 } { x } }$