How do you simplify #(3x)/(2x-5) * (-2x+5)/(6x-9x^2)#?

1 Answer
Jul 16, 2015

Answer:

#(3x)/(2x-5)*(-2x+5)/(6x-9x^2)#
#color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")##=-1/(2-3x)#

Explanation:

#(3x)/(2x-5)*(-2x+5)/(6x-9x^2)#

Extracting factors to provide equivalent expressions in numerators and denominators:
#color(white)("XXXX")##= (3x)/(2x-5) * ((-1)(2x-5))/((3x)(2-3x))#

"Cancel" equal terms from numerator and denominator
#color(white)("XXXX")##= (cancel(3x))/(cancel(2x-5)) * ((-1)(cancel(2x-5)))/((cancel(3x))(2-3x))#

Write in "clean form"
#color(white)("XXXX")##= (3x)/(2x-5) * ((-1)(2x-5))/((3x)(2-3x))##=-1/(2-3x)#