# How do I simplify this expression?

by R. Burton   Last Updated November 18, 2018 18:20 PM

How do I simplify: $$d=\frac{-(x+\alpha x)^2+(y+\alpha y)^2+2+x^2-y^2-2}{\sqrt{\alpha x^2+\alpha y^2}}$$ If simplification is possible, it should be possible with elementary algebra, but I'm completely lost as to how to go about it.

What I've done so far: $$d=\frac{-(x+\alpha x)^2+(y+\alpha y)^2+2+x^2-y^2-2}{\sqrt{\alpha x^2+\alpha y^2}}$$ $$=\frac{-(x+\alpha x)^2+(y+\alpha y)^2+x^2-y^2}{\sqrt{\alpha x^2+\alpha y^2}}=\frac{-\alpha^2x^2+\alpha^2y^2-2\alpha x+2\alpha y}{\sqrt{\alpha x^2+\alpha y^2}}$$ $$\implies d^2=\left(\frac{(-a^2x^2+a^2y^2-2ax+2ay)^2}{a^2x^2+a^2y^2}\right)^2$$

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