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

2 Answers
May 19, 2018

(-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!

May 19, 2018

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)