Example

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

Question

$$\frac{\sqrt{32}+\sqrt{48}}{\sqrt{8}+\frac{\sqrt{12}}$$

Answer

$$44*sq*r*t+384*sq*r^2*t^2*s*q$$

Solution


Regroup terms.
\[32sqrt+sqrt\times 48sqrt\times 8+sqrt\times 12\]
Take out the constants.
\[32sqrt+(48\times 8)rrttsqsq+sqrt\times 12\]
Simplify  \(48\times 8\)  to  \(384\).
\[32sqrt+384rrttsqsq+sqrt\times 12\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[32sqrt+384{r}^{2}{t}^{2}sqsq+sqrt\times 12\]
Regroup terms.
\[32sqrt+384sq{r}^{2}{t}^{2}sq+sqrt\times 12\]
Regroup terms.
\[32sqrt+384sq{r}^{2}{t}^{2}sq+12sqrt\]
Collect like terms.
\[(32sqrt+12sqrt)+384sq{r}^{2}{t}^{2}sq\]
Simplify.
\[44sqrt+384sq{r}^{2}{t}^{2}sq\]
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