Algebra Examples

$\frac{3}{\sqrt{x + 3} - \sqrt{x}}$

Step 1

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

$\frac{3}{\sqrt{x + 3} - \sqrt{x}} \cdot \frac{\sqrt{x + 3} + \sqrt{x}}{\sqrt{x + 3} + \sqrt{x}}$

Step 2

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

$\frac{3 (\sqrt{x + 3} + \sqrt{x})}{(\sqrt{x + 3} - \sqrt{x}) (\sqrt{x + 3} + \sqrt{x})}$

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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Step 4.1

Subtract $x$ from $x$ .

$\frac{3 (\sqrt{x + 3} + \sqrt{x})}{0 + 3}$

Step 4.2

Add $0$ and $3$ .

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

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

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

$\sqrt{x + 3} + \sqrt{x}$