4ab 2a 2b 2a
---------- - ---------- - ---------- = -----
a^2-b^2 a-b a+b a+b is this correct?
+26388 4ab 2a 2b 2a
---------- - ---------- - ---------- = -----
a^2-b^2 a-b a+b a+b is this correct?
\(\begin{array}{|rcll|} \hline && \frac{4ab}{a^2-b^2} -\frac{2a}{a-b} -\frac{2b}{a+b} \qquad &|\qquad a^2-b^2 = (a-b)(a+b)\\ &=& \frac{4ab}{(a-b)(a+b)} -\frac{2a}{a-b} -\frac{2b}{a+b} \\ &=& \frac{4ab}{(a-b)(a+b)} -\frac{2a}{a-b}\cdot \left( \frac{a+b}{a+b} \right) -\frac{2b}{a+b}\cdot \left( \frac{a-b}{a-b} \right)\\ &=& \frac{4ab-2a(a+b)-2b(a-b)}{(a-b)(a+b)} \qquad &|\qquad (a-b)(a+b)= a^2-b^2 \\ &=& \frac{4ab-2a(a+b)-2b(a-b)}{a^2-b^2} \\ &=& \frac{4ab-2a^2-2ab-2ab+2b^2}{a^2-b^2} \\ &=& \frac{4ab-4ab-2a^2+2b^2}{a^2-b^2} \\ &=& \frac{-2a^2+2b^2}{a^2-b^2} \\ &=& \frac{-2\cdot(a^2-b^2)}{a^2-b^2} \\ &=& -2 \\ \hline \end{array}\)
