[tex]\displaystyle\bf\\\frac{a}{a+b} -\frac{b}{b-a} -\frac{2ab}{a^{2} -b^{2} } =\frac{a}{a+b} +\frac{b}{a-b} -\frac{2ab}{(a -b)(a+b) } =\\\\\\=\frac{a\cdot(a-b)+b\cdot(a+b)-2ab}{(a-b)(a+b)} =\frac{a^{2} -ab+ab+b^{2}-2ab }{(a-b)(a+b)} =\\\\\\=\frac{a^{2} -2ab+b^{2} }{(a-b)(a+b)}=\frac{(a-b)^{2} }{(a-b)(a+b)} =\frac{a-b}{a+b}[/tex]