doprowadz do najprostszej postaci

[mat-inf]

\(\displaystyle{ [( a^{ \frac{1}{3} }- b^{ \frac{1}{3} })^{-1} (a-b)- \frac{a+b}{ a^{ \frac{1}{3} }+ b^{ \frac{1}{3} } }]*2(ab)^{- \frac{1}{3} }}\)

[justyna1985]

\(\displaystyle{ \left[( a^{ \frac{1}{3} }- b^{ \frac{1}{3} })^{-1} (a-b)- \frac{a+b}{ a^{ \frac{1}{3} }+ b^{ \frac{1}{3} } }\right]\cdot 2(ab)^{- \frac{1}{3} }=\\\\\\ =\left(\frac{(a-b)\cdot( a^{ \frac{1}{3} }+ b^{ \frac{1}{3}})}{ (a^{ \frac{1}{3} }\ - \ b^{ \frac{1}{3} })\cdot(a^{ \frac{1}{3} }\ + \ b^{ \frac{1}{3}})} \ - \ \frac{(a+b)\cdot(a^{ \frac{1}{3}} \ - \ b^{ \frac{1}{3}})}{ (a^{ \frac{1}{3} }+ b^{ \frac{1}{3} })\cdot(a^{ \frac{1}{3} }\ - \ b^{ \frac{1}{3}}) } \right) \cdot\frac{2}{(ab)^{ \frac{1}{3} }} =\\\\\\ =\left(\frac{ a^{\frac{4}{3}}+ab^{\frac{1}{3}}-a^{\frac{1}{3}}b-b^{\frac{4}{3} }-a^{\frac{4}{3}}+ab^{\frac{1}{3}}-a^{\frac{1}{3}}b+b^{\frac{4}{3}})}{ a^{ \frac{2}{3} }- b^{ \frac{2}{3} } }\right) \cdot\frac{2}{(ab)^{ \frac{1}{3} }}=\\\\\\ =\left(\frac{2ab^{\frac{1}{3}}-2a^{\frac{1}{3}}b}{ a^{ \frac{2}{3} }- b^{ \frac{2}{3} } } \right)\cdot\frac{2}{ a^{\frac{1}{3}}b^{ \frac{1}{3} }} =\left(\frac{2a^{\frac{1}{3}}b^{\frac{1}{3}}\cdot( a^{\frac{2}{3}}-b^{ \frac{2}{3} })}{a^{ \frac{2}{3} }- b^{ \frac{2}{3} } }\right)\cdot\frac{2}{ a^{\frac{1}{3}}b^{ \frac{1}{3} }}=4}\)

[mat-inf]

Dzieki