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**Lexadis** So, I was doinf this sum and got stuck in between, I'm not sure whether it's the correct answer.. so anyone please help me check it out? Thank you very much in advance :]

$\displaystyle \frac{x-y}{x^{2}+xy}+ \frac{2\left ( x+3y \right )}{x^{2}-y^{2}} = \frac{x-y}{x\left ( x+y \right )}+ \frac{2\left ( x+3y \right )}{\left ( x-y \right )\left ( x+y \right )}$

................................$\displaystyle = \frac{\left ( x-y) \right x\left ( x+y \right )+2x\left ( x+3y \right )}{x\left ( x+y \right )\left ( x-y \right )}$

................................$\displaystyle = \frac{\left ( x-y \right )\left ( x^{2}+xy \right )+2x^{2}+6xy}{x\left ( x+y \right )\left ( x-y \right )}$

................................$\displaystyle = \frac{x\left ( x^{2}+xy \right )-y\left ( x^{2} +xy\right )+2x^{2}+6xy}{x\left ( x+y \right )\left ( x-y \right )}$

................................$\displaystyle = \frac{x^{3}+x^{2}y-x^{2}y-xy^{2}+2x^{2}+6xy}{x\left ( x+y \right )\left ( x-y \right )}$

................................$\displaystyle = \frac{x^{3}-xy^{2}+2x^{2}+6xy}{x\left ( x+y \right )\left ( x-y \right )}$

................................$\displaystyle = \frac{x\left ( x^{2}-y \right )+2x\left ( x+3y \right )}{x\left ( x+y \right )\left ( x-y \right )}$

................................$\displaystyle = \frac{\left ( x^{2} -y\right )\left ( x+3y \right )\left ( x+2x \right )}{x\left ( x+y \right )\left ( x-y \right )}$

Is this correct? Or is there something wrong as I'm suspecting? Thank you for any help in advance, once again c: