Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\frac{ a-b }{ \sqrt[ 3 ]{ a } - \sqrt[ 3 ]{ b } } - \frac{ a+b }{ a \frac{ 1 }{ 3 } +b \frac{ 1 }{ 3 } }$$

Answer

$$(a-b)/(a^(1/3)-b^(1/3))-3$$

Solution


Simplify  \(a\times \frac{1}{3}\)  to  \(\frac{a}{3}\).
\[\frac{a-b}{\sqrt[3]{a}-\sqrt[3]{b}}-\frac{a+b}{\frac{a}{3}+b\times \frac{1}{3}}\]
Simplify  \(b\times \frac{1}{3}\)  to  \(\frac{b}{3}\).
\[\frac{a-b}{\sqrt[3]{a}-\sqrt[3]{b}}-\frac{a+b}{\frac{a}{3}+\frac{b}{3}}\]
Join the denominators.
\[\frac{a-b}{\sqrt[3]{a}-\sqrt[3]{b}}-\frac{a+b}{\frac{a+b}{3}}\]
Invert and multiply.
\[\frac{a-b}{\sqrt[3]{a}-\sqrt[3]{b}}-(a+b)\times \frac{3}{a+b}\]
Cancel \(a+b\).
\[\frac{a-b}{\sqrt[3]{a}-\sqrt[3]{b}}-3\]
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