Задача степен с рационален показател

[Гост]

Някой може ли да реши тази задача? (Качих снимка)

[S.B.]

[tex]\frac{a - 1}{а^{\frac{1}{3}} + 1} ( \frac{а^{\frac{1}{3}}}{а - 1} + \frac{1}{a^{\frac{1}{3}} - 1} ) =[/tex]
[tex]= \frac{a - 1}{a^{\frac{1}{3}} + 1}(\frac{a^{\frac{1}{3}}}{(a^{\frac{1}{3}})^{3} - 1^{3}} + \frac{1}{a^{\frac{1}{3}} - 1} ) =[/tex]
[tex]= \frac{a - 1}{a^{\frac{1}{3}} + 1} ( \frac{a^{\frac{1}{3}}}{(a^{\frac{1}{3}} - 1)(a^{\frac{2}{3}} + a^{\frac{1}{3}} + 1)} + \frac{1}{a^{\frac{1}{3}} - 1}) =[/tex]
[tex]= \frac{a - 1}{a^{\frac{1}{3}} + 1}( \frac{a^{\frac{1}{3}} + a^{\frac{2}{3}} + a^{\frac{1}{3}} + 1 )}{(a^{\frac{1}{3}} - 1)(a^{\frac{2}{3}} + a^{\frac{1}{3}} + 1) }
)=[/tex]
[tex]\frac{(a^{\frac{1}{3}})^{3} - 1^{3}}{a^{\frac{1}{3}} + 1} ( \frac{(a^{\frac{1}{3}})^{2} + 2a^{\frac{1}{3}} + 1^{2}}{(a^{\frac{1}{3}})^{3} - 1^{3}}) =[/tex]
[tex]= \frac{(a^{\frac{1}{3}} + 1)^{2}}{a^{\frac{1}{3}} + 1} = a^{\frac{1}{3}} + 1[/tex]

[Гост]

Благодаря!