Algebra Examples

$\sqrt{x^{2} + 5} - x$

Step 1

Multiply to rationalize the numerator.

$\frac{(\sqrt{x^{2} + 5} - x) (\sqrt{x^{2} + 5} + x)}{\sqrt{x^{2} + 5} + x}$

Step 2

Simplify.

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Step 2.1

Expand the numerator using the FOIL method.

$\frac{{\sqrt{x^{2} + 5}}^{2} + \sqrt{x^{2} + 5} x + \sqrt{x^{2} + 5} (- x) - x^{2}}{\sqrt{x^{2} + 5} + x}$

Step 2.2

Simplify.

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Step 2.2.1

Subtract $x^{2}$ from $x^{2}$ .

$\frac{0 + 5}{\sqrt{x^{2} + 5} + x}$

Step 2.2.2

Add $0$ and $5$ .

$\frac{5}{\sqrt{x^{2} + 5} + x}$