Is My Algebra Fraction Simplification Correct?

[Taylor_1989]

I would just like someone to check my math on this, because I am not sure that I am doing it the right way. I will show step by step.

Put over common denominator: $\frac{1}{x} + \frac{x}{x+y} + \frac{y}{x-y}$

1. common denominator: $\frac{x^2-y^2}{x(x^2-y^2)} + \frac{x*x(x-y)}{x(x^2-y^2)}+\frac{y*x(x+y)}{x(x^2-y^2)}$

2. adding fractions: $x^2-y^2 + x^2(x-y)+xy(x+y) \rightarrow x^2-y^2 + x^3-x^2y+x^2y+xy^2 \rightarrow x^3+x^2-y^2+xy^2$

The part I am confused with is that, I have to do the multiplication before I expand the brackets, now I thought you always expand the brackets first. This is why I think I have done the wrong method to get the right answer. Can someone set me right, if i have gone wrong somewhere. Big thanks in advanced.

 

[MarneMath]

I'm just confused, this looks right, but what do you mean by expanding the brackets? I don't see anything you have to expand.

 

[Taylor_1989]

I think I have confused myself a bit, but looking over what I have done I see where I thought I had got confuse, just ignore this post, I apologize for the inconvenience of this post.