Example

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

Question

$$\frac{3\sqrt{2}+2\sqrt{3}}{3\sqrt{2}\div2\sqrt{3}}$$

Answer

((3*sqrt(2)+2*sqrt(3))*sqrt(6))/9

Solution


Simplify  \(3\times \frac{\sqrt{2}}{2}\sqrt{3}\)  to  \(\frac{3\sqrt{2}\sqrt{3}}{2}\).
\[\frac{3\sqrt{2}+2\sqrt{3}}{\frac{3\sqrt{2}\sqrt{3}}{2}}\]
Simplify  \(3\sqrt{2}\sqrt{3}\)  to  \(3\sqrt{6}\).
\[\frac{3\sqrt{2}+2\sqrt{3}}{\frac{3\sqrt{6}}{2}}\]
Invert and multiply.
\[(3\sqrt{2}+2\sqrt{3})\times \frac{2}{3\sqrt{6}}\]
Rationalize the denominator: \((3\sqrt{2}+2\sqrt{3})\times \frac{2}{3\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}=\frac{(3\sqrt{2}+2\sqrt{3})\times 2\sqrt{6}}{3\times 6}\).
\[\frac{(3\sqrt{2}+2\sqrt{3})\times 2\sqrt{6}}{3\times 6}\]
Regroup terms.
\[\frac{2(3\sqrt{2}+2\sqrt{3})\sqrt{6}}{3\times 6}\]
Simplify  \(3\times 6\)  to  \(18\).
\[\frac{2(3\sqrt{2}+2\sqrt{3})\sqrt{6}}{18}\]
Simplify.
\[\frac{(3\sqrt{2}+2\sqrt{3})\sqrt{6}}{9}\]

Decimal Form: 2.097510

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