How do you simplify #\frac { 46x ^ { 3} y + 38x ^ { 2} y ^ { 2} } { 2x ^ { 2} y }#?

1 Answer
smendyka
Dec 4, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#(46x^3y)/(2x^2y) + (38x^2y^2)/(2x^2y)#

#(23x^3y)/(x^2y) + (19x^2y^2)/(x^2y)#

Next, cancel any common terms in each of the fractions:

#(23x^3color(red)(cancel(color(black)(y))))/(x^2color(red)(cancel(color(black)(y)))) + (19color(red)(cancel(color(black)(x^2)))y^2)/(color(red)(cancel(color(black)(x^2)))y)#

#(23x^3)/x^2 + (19y^2)/y#

Next, use these rules of exponents to complete the simplification:

  • #a = a^color(blue)(1)#
  • #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#
  • #a^color(red)(1) = a#

#(23x^color(red)(3))/x^color(blue)(2) + (19y^color(red)(2))/y^color(blue)(1)#

#23x^(color(red)(3)-color(blue)(2)) + 19y^(color(red)(2)-color(blue)(1))#

#23x^1 + 19y^1#

#23x + 19y#

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