Пожалуйста, помогите. Даю 50 баллов Cократите дробь:. Created by manekinika. algebra-ru

Пожалуйста, помогите. Даю 50 баллов Cократите дробь:...

m11m

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Объяснение:

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2 votes Thanks 1

manekinika Спасибо огромное, Вы просто спасаете меня)

kamilmatematik100504

Сократить дробь :

$\large \boldsymbol {} \displaystyle \frac{\sqrt{c} -\sqrt[3]{d^2} }{\sqrt[4]{c} -\sqrt[3]{d} }$

Сделаем замену :

$\large \boldsymbol {} \displaystyle \sqrt[4]{c} =x \ \ ; \ \ \sqrt{c} =x ^2 \\\\\\ \sqrt[3]{b} =y \ \ ; \ \ \sqrt[3]{b^2} =y^2$

Подставим значения :

$\large \boldsymbol {} \displaystyle \frac{x^2-y^2}{x-y }$

Воспользуемся формулой :

$\large \boldsymbol {} \displaystyle a^2-b^2=(a+b)(a-b)$

Сократим дробь :

$\large \boldsymbol {} \displaystyle \frac{x^2-y^2}{x-y }=\frac{(x+y)\!\!\!\!\!\! \Big/(x-y)}{(x+y)\!\!\!\!\!\! \Big/} =x-y =\boxed{ \sqrt[4]{c} - \sqrt[3]{b} }$

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