Algebra Problem regarding simplifying

Solid8Snake · #1 $Old$ August 23rd, 2009, 09:24 AM

I am having difficulty simplifying this question, any assistance would be greatly appreciated.

Thx in advance.

skeeter · #2 $Old$ August 23rd, 2009, 09:38 AM

$\frac{x+y}{2(x^2+y^2)} - \frac{1}{2(x+y)} + \frac{x-y}{x^2-y^2} - \frac{x^3-y^3}{x^4-y^4}$

$\frac{x+y}{2(x^2+y^2)} - \frac{1}{2(x+y)} + \frac{x-y}{(x-y)(x+y)} - \frac{(x-y)(x^2+xy+y^2)}{(x+y)(x-y)(x^2+y^2)}$

$\frac{x+y}{2(x^2+y^2)} - \frac{1}{2(x+y)} + \frac{1}{x+y} - \frac{x^2+xy+y^2}{(x+y)(x^2+y^2)}$

common denominator is $2(x+y)(x^2+y^2)$ ...

$\frac{(x+y)^2}{2(x+y)(x^2+y^2)} - \frac{x^2+y^2}{2(x+y)(x^2+y^2)} + \frac{2(x^2+y^2)}{2(x+y)(x^2+y^2)} - \frac{2(x^2+xy+y^2)}{2(x+y)(x^2+y^2)}$

I'll leave you to finish up the grunt work of adding/simplifying the terms in the numerator.