Algebra Examples

$\frac{\sqrt{12 x + 15 x^{2}}}{\sqrt{3 x}}$

Step 1

Factor $3 x$ out of $12 x + 15 x^{2}$ .

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Step 1.1

Factor $3 x$ out of $12 x$ .

$\frac{\sqrt{3 x (4) + 15 x^{2}}}{\sqrt{3 x}}$

Step 1.2

Factor $3 x$ out of $15 x^{2}$ .

$\frac{\sqrt{3 x (4) + 3 x (5 x)}}{\sqrt{3 x}}$

Step 1.3

Factor $3 x$ out of $3 x (4) + 3 x (5 x)$ .

$\frac{\sqrt{3 x (4 + 5 x)}}{\sqrt{3 x}}$

Step 2

Combine $\sqrt{3 x (4 + 5 x)}$ and $\sqrt{3 x}$ into a single radical.

$\sqrt{\frac{3 x (4 + 5 x)}{3 x}}$

Step 3

Reduce the expression $\frac{3 x (4 + 5 x)}{3 x}$ by cancelling the common factors.

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{3 x (4 + 5 x)}{3 x}}$

Step 3.2

Rewrite the expression.

$\sqrt{\frac{x (4 + 5 x)}{x}}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

$\sqrt{\frac{x (4 + 5 x)}{x}}$

Step 4.2

Divide $4 + 5 x$ by $1$ .

$\sqrt{4 + 5 x}$