Algebra Examples

$\frac{\sqrt{x + 5} - 2}{x + 1}$

Step 1

Multiply to rationalize the numerator.

$\frac{(\sqrt{x + 5} - 2) (\sqrt{x + 5} + 2)}{(x + 1) (\sqrt{x + 5} + 2)}$

Step 2

Simplify.

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Step 2.1

Expand the numerator using the FOIL method.

$\frac{{\sqrt{x + 5}}^{2} + \sqrt{x + 5} \cdot 2 + \sqrt{x + 5} \cdot - 2 - 4}{(x + 1) (\sqrt{x + 5} + 2)}$

Step 2.2

Simplify.

$\frac{x + 1}{(x + 1) (\sqrt{x + 5} + 2)}$

Step 3

Expand $(x + 1) (\sqrt{x + 5} + 2)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$\frac{x + 1}{x (\sqrt{x + 5} + 2) + 1 (\sqrt{x + 5} + 2)}$

Step 3.2

Apply the distributive property.

$\frac{x + 1}{x \sqrt{x + 5} + x \cdot 2 + 1 (\sqrt{x + 5} + 2)}$

Step 3.3

Apply the distributive property.

$\frac{x + 1}{x \sqrt{x + 5} + x \cdot 2 + 1 \sqrt{x + 5} + 1 \cdot 2}$

Step 4

Simplify each term.

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Step 4.1

Move $2$ to the left of $x$ .

$\frac{x + 1}{x \sqrt{x + 5} + 2 \cdot x + 1 \sqrt{x + 5} + 1 \cdot 2}$

Step 4.2

Multiply $\sqrt{x + 5}$ by $1$ .

$\frac{x + 1}{x \sqrt{x + 5} + 2 x + \sqrt{x + 5} + 1 \cdot 2}$

Step 4.3

Multiply $2$ by $1$ .

$\frac{x + 1}{x \sqrt{x + 5} + 2 x + \sqrt{x + 5} + 2}$