SOLUTION: [(x/y)-(y/x]/[(1/y)+(1/x)] when i use the LCD method i get (x-y)/2 and i know the correct answer is x-y. can you simplify with the LCD method so that i can see what i am doing wron

Question 858296: [(x/y)-(y/x]/[(1/y)+(1/x)] when i use the LCD method i get (x-y)/2 and i know the correct answer is x-y. can you simplify with the LCD method so that i can see what i am doing wrong. thank you, todd.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We are asked to simplify
[(x/y)-(y/x]/[(1/y)+(1/x)]
numerator LCD is xy and denominator LCD is xy
[(x^2 - y^2) / xy] / [ (x + y) / xy ]
now invert the denominator and multiply by numerator, also factor numerator
[ (x+y)*(x-y) / xy ] * [ xy / (x + y ) ]
the xy terms cancel and the (x + y) terms cancel
answer is (x - y)

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