Find all asymptotes of given curve y^2(a+x)=x^2(a−x) origin i found will be a node i'm trying to find asymptotes by equating highest degree term to 0 Please help.

write $y(x)=mx+b$ and then rearrange equation in the form $\sum _0^n{a}_n{x}^n=0$, where n is the highest degree term you get once you rearrange equation.
Now you set $a_n$ and $a_{n-1}$ to 0 and for each pair {m,b} found you get an asymptote. in your case if i didn't make any mistakes you should find only one asymptote at x=−a