Algebra Examples

$\frac{4}{\sqrt{x - 2} - \sqrt{x}}$

Step 1

Multiply $\frac{4}{\sqrt{x - 2} - \sqrt{x}}$ by $\frac{\sqrt{x - 2} + \sqrt{x}}{\sqrt{x - 2} + \sqrt{x}}$ .

$\frac{4}{\sqrt{x - 2} - \sqrt{x}} \cdot \frac{\sqrt{x - 2} + \sqrt{x}}{\sqrt{x - 2} + \sqrt{x}}$

Step 2

Multiply $\frac{4}{\sqrt{x - 2} - \sqrt{x}}$ by $\frac{\sqrt{x - 2} + \sqrt{x}}{\sqrt{x - 2} + \sqrt{x}}$ .

$\frac{4 (\sqrt{x - 2} + \sqrt{x})}{(\sqrt{x - 2} - \sqrt{x}) (\sqrt{x - 2} + \sqrt{x})}$

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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Step 4.1

Subtract $x$ from $x$ .

$\frac{4 (\sqrt{x - 2} + \sqrt{x})}{0 - 2}$

Step 4.2

Subtract $2$ from $0$ .

$\frac{4 (\sqrt{x - 2} + \sqrt{x})}{- 2}$

Step 5

Cancel the common factor of $4$ and $- 2$ .

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Step 5.1

Factor $2$ out of $4 (\sqrt{x - 2} + \sqrt{x})$ .

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

Step 5.2

Move the negative one from the denominator of $\frac{2 (\sqrt{x - 2} + \sqrt{x})}{- 1}$ .

$- 1 \cdot (2 (\sqrt{x - 2} + \sqrt{x}))$

Step 6

Rewrite $- 1 \cdot (2 (\sqrt{x - 2} + \sqrt{x}))$ as $- (2 (\sqrt{x - 2} + \sqrt{x}))$ .

$- (2 (\sqrt{x - 2} + \sqrt{x}))$

Step 7

Apply the distributive property.

$- (2 \sqrt{x - 2} + 2 \sqrt{x})$

Step 8

Apply the distributive property.

$- (2 \sqrt{x - 2}) - (2 \sqrt{x})$

Step 9

Multiply.

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Step 9.1

Multiply $2$ by $- 1$ .

$- 2 \sqrt{x - 2} - (2 \sqrt{x})$

Step 9.2

Multiply $2$ by $- 1$ .

$- 2 \sqrt{x - 2} - 2 \sqrt{x}$