Simplify.
-$\frac { 1 - \frac { 2 } { x } } { x - \frac { 4 } { x } }$
A) $x + 2$
B) $\frac { 1 } { x + 2 }$
C) $\frac { 1 } { x - 2 }$
D) $x - 2$

Question

Quizplus · Accepted Answer

To simplify the given expression, first find a common denominator for the fractions in the numerator and the denominator. The common denominator is $x$, so rewrite the expression as $\frac { \frac { x - 2 } { x } } { \frac { x^2 - 4 } { x } }$. Simplify the complex fraction by multiplying the numerator and the denominator by $x$, which gives $\frac { x - 2 } { x^2 - 4 }$. Factor the denominator as a difference of squares, $x^2 - 4 = (x + 2)(x - 2)$, so the expression becomes $\frac { x - 2 } { (x + 2)(x - 2) }$. Cancel out $x - 2$ from the numerator and the denominator, leaving $\frac { 1 } { x + 2 }$.

Simplify - 1−2xx−4x\frac { 1 - \frac { 2 } { x } } { x - \frac { 4 } { x } }x−x4​1−x2​​

Simplify
- $\frac { 1 - \frac { 2 } { x } } { x - \frac { 4 } { x } }$