Question

Упростит выражение, если y>0

Answer 1

$\frac{\sqrt{1-4y^2}-1}{2y}*\frac{\sqrt{1+2y}+\sqrt{1-2y}}{\sqrt{1-2y}-\sqrt{1+2y}}=\frac{\sqrt{1-4y^2}-1}{2y}*\frac{(\sqrt{1+2y}+\sqrt{1-2y})^2}{(\sqrt{1-2y}-\sqrt{1+2y})(\sqrt{1-2y}+\sqrt{1+2y})}=\\=\frac{\sqrt{1-4y^2}-1}{2y}*\frac{1+2y+2\sqrt{1+2y}\sqrt{1-2y}+1-2y}{1-2y-1-2y}=\frac{\sqrt{1-4y^2}-1}{2y}*\frac{2+2\sqrt{1+2y}\sqrt{1-2y}}{-4y}=\\=\frac{\sqrt{1-4y^2}-1}{2y}*\frac{\sqrt{1-4y^2}+1}{-2y}=\frac{1-4y^2-1}{-4y^2}=\frac{-4y^2}{-4y^2}=1$