Basic Math Examples

$\frac{3 \sqrt{y}}{2 \sqrt{y - 3}}$

Step 1

Multiply $\frac{3 \sqrt{y}}{2 \sqrt{y - 3}}$ by $\frac{\sqrt{y - 3}}{\sqrt{y - 3}}$ .

$\frac{3 \sqrt{y}}{2 \sqrt{y - 3}} \cdot \frac{\sqrt{y - 3}}{\sqrt{y - 3}}$

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{3 \sqrt{y}}{2 \sqrt{y - 3}}$ by $\frac{\sqrt{y - 3}}{\sqrt{y - 3}}$ .

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 \sqrt{y - 3} \sqrt{y - 3}}$

Step 2.2

Move $\sqrt{y - 3}$ .

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 (\sqrt{y - 3} \sqrt{y - 3})}$

Step 2.3

Raise $\sqrt{y - 3}$ to the power of $1$ .

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 ({\sqrt{y - 3}}^{1} \sqrt{y - 3})}$

Step 2.4

Raise $\sqrt{y - 3}$ to the power of $1$ .

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 ({\sqrt{y - 3}}^{1} {\sqrt{y - 3}}^{1})}$

Step 2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 {\sqrt{y - 3}}^{1 + 1}}$

Step 2.6

Add $1$ and $1$ .

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 {\sqrt{y - 3}}^{2}}$

Step 2.7

Rewrite ${\sqrt{y - 3}}^{2}$ as $y - 3$ .

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Step 2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y - 3}$ as ${(y - 3)}^{\frac{1}{2}}$ .

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 {({(y - 3)}^{\frac{1}{2}})}^{2}}$

Step 2.7.2

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

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 {(y - 3)}^{\frac{1}{2} \cdot 2}}$

Step 2.7.3

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

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 {(y - 3)}^{\frac{2}{2}}}$

Step 2.7.4

Cancel the common factor of $2$ .

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Step 2.7.4.1

Cancel the common factor.

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 {(y - 3)}^{\frac{2}{2}}}$

Step 2.7.4.2

Rewrite the expression.

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 {(y - 3)}^{1}}$

Step 2.7.5

Simplify.

$\frac{3 \sqrt{y} \sqrt{y - 3}}{2 (y - 3)}$

Step 3

Combine using the product rule for radicals.

$\frac{3 \sqrt{(y - 3) y}}{2 (y - 3)}$

Step 4

Reorder factors in $\frac{3 \sqrt{(y - 3) y}}{2 (y - 3)}$ .

$\frac{3 \sqrt{y (y - 3)}}{2 (y - 3)}$