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Topic: Combining Fractions
Replies: 2   Last Post: Jun 20, 2013 5:19 AM

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Posts: 132
Registered: 11/27/12
Re: Combining Fractions
Posted: Jun 18, 2013 9:03 AM
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> Hello,
> I'm trying to solve a problem but I can't seem to get
> the answer correct.
> The problem is:
> ((x+y)/(x-y)) + (1/(x+y)) - ((x^2+y^2)/(y^2-x^2))
> When I try to solve the problem, first thing I do is
> flip the sign of the last fractions numerator to flip
> the denominator so I can have a LCD.
> ((x+y)/(x-y)) + (1/(x+y)) + ((x^2+y^2)/(x^2-y^2))
> Then I apply the LCD:
> ((x+y)(x-y)) + x+y + (x^2+y^2)) / x^2-y^2
> Then simplify terms:
> x^2-y^2 + x+y + (x^2+y^2)) / x^2-y^2

You have an error here. The denominator in the middle term is (x+ y) so you need to multiply the numerator and denominator by x- y. you should have
x^2- y^2+ x- y+ (x^2+ y^2)/x^2- y^2

> Then I eliminate the x^2-y^2 from the equation:
> x+y + (x^2+y^2)
> I know this is grossly incorrect, I tried several
> different ways of solving this problem and I'm not
> even close. Any help will be appreciated.

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