Question

How do you divide `(5x+15)/(12x-6) div(10x^2)/(18)`?

Answer 1

`3/2 * (x+3)/(x-2) * 1/x^2`

Explanation:

Your starting expression looks like this

`(5x + 15)/(12x-6) * 18/(10x^2)`

Factor the numerator and the denominator of the first fraction to get

`(5(x + 3))/(6(x-2))`

The expression will now become

`(color(red)(cancel(color(black)(5)))(x+3))/(color(red)(cancel(color(black)(6)))(x-2)) * (color(red)(cancel(color(black)(18)))3)/(color(red)(cancel(color(black)(10)))2x^2)`

`(x+3)/(x-2) * 3/(2x^2) = color(green)(3/2 * (x+3)/(x-2) * 1/x^2)`