Precalculus Examples

$\frac{\sqrt{x + 8} - \sqrt{8}}{\sqrt{x + 8} + \sqrt{8}}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$\frac{\sqrt{x + 8} - \sqrt{4 (2)}}{\sqrt{x + 8} + \sqrt{8}}$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{x + 8} - \sqrt{2^{2} \cdot 2}}{\sqrt{x + 8} + \sqrt{8}}$

Step 2

Pull terms out from under the radical.

$\frac{\sqrt{x + 8} - (2 \sqrt{2})}{\sqrt{x + 8} + \sqrt{8}}$

Step 3

Multiply $2$ by $- 1$ .

$\frac{\sqrt{x + 8} - 2 \sqrt{2}}{\sqrt{x + 8} + \sqrt{8}}$

Step 4

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 4.1

Factor $4$ out of $8$ .

$\frac{\sqrt{x + 8} - 2 \sqrt{2}}{\sqrt{x + 8} + \sqrt{4 (2)}}$

Step 4.2

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{x + 8} - 2 \sqrt{2}}{\sqrt{x + 8} + \sqrt{2^{2} \cdot 2}}$

Step 5

Pull terms out from under the radical.

$\frac{\sqrt{x + 8} - 2 \sqrt{2}}{\sqrt{x + 8} + 2 \sqrt{2}}$