> 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.