Question

How do you simplify `\frac { \frac { 1} { 2} - \frac { 1} { x } } { \frac { x } { 2} - 1}`?

Answer 1

`1/x`

Explanation:

Given: `(1/2 - 1/x)/(x/2-1)`

Find common denominators for both numerator and denominator:

`(1/2 *x/x - 1/x*2/2)/(x/2-2/2) = ((x-2)/(2x))/((x-2)/2)`

A division of a fraction can be changed to multiplication if you multiply by the reciprocal of the denominator:

`((x-2)/(2x))/((x-2)/2) = cancel(x-2)/(2x) * 2/cancel(x-2) = cancel(2)/(cancel(2)x) = 1/x`