Basic Algebra combining exponent fractions/simplifying (George F Simmons "Precalculus in Nutshell")

migongoniwt

migongoniwt

Answered question

2022-06-15

Basic Algebra combining exponent fractions/simplifying (George F Simmons "Precalculus in Nutshell")
From George F. Simmons 'Precalculus' book, Algebra section, 5(d); Combine and Simplify
x x y 2 + y x 2 y
Combine: =
x ( x 2 y ) + y ( x y 2 ) ( x y 2 ) ( x 2 y )
Simplify: =
x ( x 2 y ) + y ( x y 2 ) x y ( x 2 y 2 )
The given answer, which I can't figure out how he arrives at it is:
x 2 + y 2 x 2 y 2

Answer & Explanation

victorollaa5

victorollaa5

Beginner2022-06-16Added 16 answers

x x y 2 + y x 2 y = x x x x y 2 + y y y x 2 y = x x x y 2 x + y y x 2 y y = x 2 x 2 y 2 + y 2 x 2 y 2 = x 2 + y 2 x 2 y 2
kokoszzm

kokoszzm

Beginner2022-06-17Added 8 answers

We have: x x y 2 + y x 2 y
= x ( x 2 y ) + y ( x y 2 ) ( x y 2 ) ( x 2 y )
= x ( x 2 y ) + y ( x y 2 ) x y ( x 2 y 2 )
This is where you got stuck, but there is not much left to do to arrive at that result.
= x 3 y + y 3 x x y ( x 2 y 2 )
= x y ( x 2 + y 2 ) x y ( x 2 y 2 )
= x 2 + y 2 x 2 y 2

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