Question

How do you multiply and simplify `\frac { 8} { x - 7} \cdot \frac { 7- x } { 16x }`?

Answer 1

See a solution process below:

Explanation:

First, multiply the fraction on the right by `(-1)/(-1)` which is a form of `1` and therefore does not change the value of the fraction:

`8/(x - 7) * ((-1)/-1 * (7 - x)/(16x)) =>`

`8/(x - 7) * (-1(7 - x))/(-16x) =>`

`8/(x - 7) * ((-1 xx 7) - (-1 xx x))/(-16x) =>`

`8/(x - 7) * (-7 - (-x))/(-16x) =>`

`8/(x - 7) * (-7 + x)/(-16x) =>`

`8/(x - 7) * (x - 7)/(-16x)`

Now, cancel common terms in the numerator and the denominator:

`color(blue)(cancel(color(black)(8)))/color(red)(cancel(color(black)(x - 7))) * color(red)(cancel(color(black)(x - 7)))/(-color(blue)(cancel(color(black)(16)))2x) =>`

`-1/(2x)`