Математика, вопрос задал barinovaoxana , 9 лет назад

Упростить ( (a^2-ab)(a^-0,5+b^-0,5) ) / ( (a+b+2sqrt(ab)) * (a^-0,5-b^-0,5) )

Ответы на вопрос

Ответил АннаАрт

$frac{(a^2-ab)*(frac{1}{sqrt{a}}+frac{1}{sqrt{b}})}{(a+b+2sqrt{ab})*(frac{1}{sqrt{a}}-frac{1}{sqrt{b}})}$

$1) (a^2-ab)*(frac{1}{sqrt{a}}+frac{1}{sqrt{b}})=a(a-b)*(frac{sqrt{a}+sqrt{b}}{sqrt{a}sqrt{b}})=frac{a(a-b)(sqrt{a}+sqrt{b})}{sqrt{a}sqrt{b}}$

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

$3) frac{a(a-b)(sqrt{a}+sqrt{b})}{sqrt{a}sqrt{b}}:(-frac{(sqrt{a}+sqrt{b})^2(sqrt{a}-sqrt{b})}{sqrt{a}sqrt{b}})= \ \ =frac{a(a-b)(sqrt{a}+sqrt{b})}{sqrt{a}sqrt{b}}*(-frac{sqrt{a}sqrt{b}}{(sqrt{a}+sqrt{b})^2(sqrt{a}-sqrt{b})})= \ \ =-frac{a(a-b)}{(sqrt{a}+sqrt{b})(sqrt{a}-sqrt{b})}=-frac{a(a-b)}{(a-b)}=-a$