Question

Упростить!
$frac{a sqrt{a}+b sqrt{b}}{(sqrt{a} + sqrt{b})(a-b)}+ frac{2 sqrt{b} }{ sqrt{a} + sqrt{b}}- frac{sqrt{ab} }{a-b}$

Answer 1

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

Answer 2

Благодарю!