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

2 Answers
May 19, 2018

Answer:

#(-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

Answer:

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)#