Question

How do you multiply and simplify `\frac { 6x - 12} { 9x - 36} \cdot \frac { x - 4} { x - 2}`?

Answer 1

See a solution process below:

Explanation:

First factor the numerator and denominator of the fraction on the left as:

`(6x - 12)/(9x - 36) * (x - 4)/(x - 2) =>`

`([6 * x] - [6 * 2])/([9 * x] - [9 * 4]) * (x - 4)/(x - 2) =>`

`(6(x - 2))/(9(x - 4)) * (x - 4)/(x - 2)`

Next, cancel common terms across the numerators and denominators:

`(6color(red)(cancel(color(black)((x - 2)))))/(9color(orange)(cancel(color(black)((x - 4))))) * color(orange)(cancel(color(black)(x - 4)))/color(red)(cancel(color(black)(x - 2))) => 6/9`

We can now reduce the remaining fraction:

`(3 * 2)/(3 * 3) => (color(red)(cancel(color(black)(3))) * 2)/(color(red)(cancel(color(black)(3))) * 3) => 2/3`