How about this? $\displaystyle \frac{a-b}{a+b+2a^{\frac{1}{2}}b^{\frac{1}{2}}}:\frac{a^{-\frac{1}{2}}-b^{-\frac{1}{2}}}{a^{-\frac{1}{2}}+b^{-\frac{1}{2}}}$
$\displaystyle ...=\frac{(a-b)*(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})^2*(\sq rt{a}-\sqrt{b})}=\frac{(a-b)}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})}=\frac{a-b}{a-b}=1$
But answer have to be -1. What's wrong?
$\displaystyle ...=\frac{(a-b)*(\sqrt{a}+\sqrt{b})}{(\sqrt{a}+\sqrt{b})^2*(\sq rt{a}-\sqrt{b})}=\frac{(a-b)}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})}=\frac{a-b}{a-b}=1$
But answer have to be -1. What's wrong?