Question

(√a+√b)/(a-b)-1/(√a-√b) спростити вираз

Answer 1

$\dfrac{\sqrt{a}+\sqrt{b}}{a-b}-\dfrac{1}{\sqrt{a}-\sqrt{b}}=\dfrac{\sqrt{a}+\sqrt{b}}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})}-\dfrac{1}{\sqrt{a}-\sqrt{b}}=\\ \\ =\dfrac{1}{\sqrt{a}-\sqrt{b}}-\dfrac{1}{\sqrt{a}-\sqrt{b}}=0$

Answer 2

$\frac{ \sqrt{a} + \sqrt{b} }{a-b} - \frac{1}{ \sqrt{a} - \sqrt{b} } =$

$\frac{ \sqrt{a} + \sqrt{b} }{a-b} - \frac{1}{ \sqrt{a} - \sqrt{b} } \cdot \frac{ \sqrt{a} + \sqrt{b}}{ \sqrt{a} + \sqrt{b}} =$

$\frac{ \sqrt{a} + \sqrt{b} }{a-b} - \frac{\sqrt{a} + \sqrt{b} }{a-b} =$

$\frac{ \sqrt{a} + \sqrt{b} - \sqrt{a} - \sqrt{b} } {a-b} =0$