Question

Ребят плиз срочно
На фото условие

Answer 1

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

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