6) $\dfrac{y^{1/3}z^{1/2}-z}{y^{2/3}-z}+\dfrac{y}{y+y^{2/3}z^{1/2}}$

Question

Вопрос: $Фото задания: 6) $\dfrac{y^{1/3}z^{1/2}-z}{y^{2/3}-z}+\dfrac{y}{y+y^{2/3}z^{1/2}}$$ Фото задания

Accepted Answer

Вынесем множители и разложим знаменатели:

\[\frac{y^{1/3}z^{1/2}-z}{y^{2/3}-z}=\frac{z^{1/2}(y^{1/3}-1)}{(y^{1/3}-z^{1/2})(y^{1/3}+z^{1/2})},\]

\[\frac{y}{y+y^{2/3}z^{1/2}}=\frac{y^{1/3}}{y^{1/3}+z^{1/2}}.\]

Приведём к общему знаменателю:

\[\frac{z^{1/2}(y^{1/3}-1)+y^{1/3}(y^{1/3}-z^{1/2})}{(y^{1/3}-z^{1/2})(y^{1/3}+z^{1/2})}=\frac{y^{2/3}-z^{1/2}}{y^{2/3}-z}.\]

Ответ: $\dfrac{y^{2/3}-z^{1/2}}{y^{2/3}-z}$.

6) \(\dfrac{y^{1/3}z^{1/2}-z}{y^{2/3}-z}+\dfrac{y}{y+y^{2/3}z^{1/2}}\)