How do you simplify #(x^2 y^3 + x y^2) / (xy)#?

2 Answers
smendyka
Mar 9, 2018

See a solution process below:

Explanation:

First, rewrite the expression as:

#(x^2y^3)/(xy) + (xy^2)/(xy)#

Now, cancel common terms in the numerators and denominators:

#(x^(color(red)(cancel(color(black)(2)))1)y^(color(blue)(cancel(color(black)(3)))2))/(color(red)(cancel(color(black)(x)))color(blue)(cancel(color(black)(y)))) + (color(green)(cancel(color(black)(x)))y^(color(purple)(cancel(color(black)(2)))1))/(color(green)(cancel(color(black)(x)))color(purple)(cancel(color(black)(y)))) =>#

#x^1y^2 + y =>#

#xy^2 + y# Where #x != 0# and #y != 0#

Or

#y(xy + 1)# Where #x != 0# and #y != 0#

sankarankalyanam
Mar 9, 2018

#color(blue)(=> y(xy +1)#

Explanation:

# (x^2y^3 + x y^2) / (xy)#

#=>( (xy)(xy^2 + y)) / (xy)# taking common term (xy) outside.

#=> (cancel(xy) * (xy^2 + y)) / cancel(xy)#

#=> y(xy +1)# taking “y” outside as common.

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