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I would like to know if its possible to pull $a$ out of the following equation without multiplying $b$ by $(x-y)$

$$ \frac{ 2a(x^2 - y^2)}{x - y} = b $$

Its part of a more complex problem I'm stuck on.


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Notice $x^2-y^2=(x+y)(x-y)$. – Jacqueline Pauwels Jul 9 '12 at 2:19
I'm not really sure what you're asking for. Perhaps $$\frac{2(x^2-y^2)}{(x-y)}=\frac{b}{a}$$ is what you want? – Alex Becker Jul 9 '12 at 2:19
Awesome, thanks Jakucha. What if the - was a + $$ \frac{ 2a(x^2 + y^2) }{ (x + y)} $$ Is it possible to pull a out without multiplying or dividing b – user346443 Jul 9 '12 at 2:34
If by "pull $a$ out" you mean, "solve $2a(x^2+y^2)/(x+y)=b$ for $a$" then the answer is no. – Gerry Myerson Jul 9 '12 at 6:13
up vote 1 down vote accepted

Yes indeed, you have the identity $$ x^2 - y^2 = (x-y)(x+y) $$ So, $$\dfrac{2a (x^2-y^2)}{x-y}=b \Leftrightarrow 2a(x+y)=b $$

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