Question

Ребят плиз срочно
На фото условие

Answer 1

$(\frac{a\sqrt{a}+b\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\sqrt{ab} )\times \frac{1}{a-b} +\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}} =\frac{a\sqrt{a}+b\sqrt{b}-a\sqrt{b}-b\sqrt{a}}{(\sqrt{a}+\sqrt{b})(a-b)} +\frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}} =\\\\ =\frac{(\sqrt{a}-\sqrt{b})(a-b)}{(a-b)(\sqrt{a}+\sqrt{b})}+ \frac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}} =\frac{\sqrt{a}-\sqrt{b}+2\sqrt{b}}{\sqrt{a}+\sqrt{b}} = \frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}+\sqrt{b}} =1$

Answer 2

1)(a√a+b√b-a√b-b√a)/(√a+√b) = (a√a-a√b)-(b√a-b√b) /(√a+√b)=

=a(√a-√b)-b(√a-√b) / (√a+√b) = (√a-√b)(a-b)/(√a+√b)

2)(√a-√b)(a-b)/(√a+√b) * 1/(a-b)=(√a-√b)/(√a+√b)

3)(√a-√b)/(√a+√b) + 2√b/(√a+√b) = (√a-√b+2√b) / (√a+√b) =

=(√a+√b)/(√a+√b)=1