Algebraic fractions - help me figure out where I have gone wrong? Thank you c:

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:

Re: Algebraic fractions - help me figure out where I have gone wrong? Thank you c:

Quote:

Originally Posted by

**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:

You are correct up until trying to go from the second-last line to the last line. There are not any common factors in what you wrote so you can not factorise as you did.

Re: Algebraic fractions - help me figure out where I have gone wrong? Thank you c:

Quote:

Originally Posted by

**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:

Your first equation contains an obvious error