How do you multiply #(6x^2y^2)/(x-2) div (3xy^2)/(x-2)^2#?

1 Answer
Jim G.
Nov 1, 2017

#2x(x-2)=2x^2-4x#

Explanation:

#"to change division to multiplication note that"#

#•color(white)(x)a/b-:c/d=a/bxxd/c#

#rArr(6x^2y^2)/(x-2)-:(3xy^2)/((x-2)^2)#

#=(6x^2y^2)/(x-2)xx((x-2)^2)/(3xy^2)#

#"now "color(blue)"cancel"" common factors on the"#
#"numerators/denominators of the fractions"#

#=(cancel(color(red)(6))^2cancel(color(blue)(x^2))^x cancel(color(magenta)(y^2))^1)/cancel((x-2)^1)xxcancel((x-2)^((x-2)))/(cancel(color(red)(3))^1cancel(color(blue)(x))^1cancel(color(magenta)(y^2))^1)#

#=(2x(x-2))/1=2x^2-4x#

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