Question

How do you simplify `(2x - 3)/(1-5x) *( 5x-1)/(2x+3)`?

Answer 1

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

Explanation:

First you want to do is times the numerators and the denominators together.. You can do this by multiplying the denominators together.
`((2x-3)(5x-1))/((1-5x)(2x+3))`
Then you can multiply both sides by `-1`
`(-(2x-3)(5x-1))/(-(1-5x)(2x+3))`
Simplify this:
`((-2x+3)(5x-1))/((5x-1)(2x+3))`
Then simplify out the `5x-1` to get
`(-2x+3)/(2x+3)`

You can't simplify this anymore so it is your answer!

Answer 2

See a solution process below:

Explanation:

First, multiply the fraction on the left by a `(-1)/-1` which is a form of `1`. This will not change the value of the fraction but it will allow us to simplify the expression:

`((-1)/-1 * (2x - 3)/(1 - 5x)) * (5x - 1)/(2x + 3) =>`

`(-1(2x - 3))/(-1(1 - 5x)) * (5x - 1)/(2x + 3) =>`

`(-2x + 3)/(-1 + 5x) * (5x - 1)/(2x + 3) =>`

`(3 - 2x)/(5x - 1) * (5x - 1)/(2x + 3)`

Now, cancel common terms in the numerator an denominator:

`(3 - 2x)/color(red)(cancel(color(black)(5x - 1))) * color(red)(cancel(color(black)(5x - 1)))/(2x + 3) =>`

`(3 - 2x)/1 * 1/(2x + 3) =>`

`((3 - 2x) * 1)/(1 * (2x + 3)) =>`

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