Basic Math Examples

$\frac{9 - r}{3 - \sqrt{r}}$

Step 1

Multiply $\frac{9 - r}{3 - \sqrt{r}}$ by $\frac{3 + \sqrt{r}}{3 + \sqrt{r}}$ .

$\frac{9 - r}{3 - \sqrt{r}} \cdot \frac{3 + \sqrt{r}}{3 + \sqrt{r}}$

Step 2

Multiply $\frac{9 - r}{3 - \sqrt{r}}$ by $\frac{3 + \sqrt{r}}{3 + \sqrt{r}}$ .

$\frac{(9 - r) (3 + \sqrt{r})}{(3 - \sqrt{r}) (3 + \sqrt{r})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{(9 - r) (3 + \sqrt{r})}{9 + 3 \sqrt{r} - 3 \sqrt{r} - {\sqrt{r}}^{2}}$

Step 4

Simplify.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{r}$ as $r^{\frac{1}{2}}$ .

$\frac{(9 - r) (3 + \sqrt{r})}{9 - {(r^{\frac{1}{2}})}^{2}}$

Step 4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{(9 - r) (3 + \sqrt{r})}{9 - r^{\frac{1}{2} \cdot 2}}$

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{(9 - r) (3 + \sqrt{r})}{9 - r^{\frac{2}{2}}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$\frac{(9 - r) (3 + \sqrt{r})}{9 - r^{\frac{2}{2}}}$

Step 4.4.2

Rewrite the expression.

$\frac{(9 - r) (3 + \sqrt{r})}{9 - r^{1}}$

Step 4.5

Simplify.

$\frac{(9 - r) (3 + \sqrt{r})}{9 - r}$

Step 5

Cancel the common factor of $9 - r$ .

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Step 5.1

Cancel the common factor.

$\frac{(9 - r) (3 + \sqrt{r})}{9 - r}$

Step 5.2

Divide $3 + \sqrt{r}$ by $1$ .

$3 + \sqrt{r}$