Calculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

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

Step 4.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

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

Step 4.4.2

Rewrite the expression.

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

Step 4.5

Simplify.

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

Step 5

Cancel the common factor of $x - 4$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $\sqrt{x} + 2$ by $1$ .

$\sqrt{x} + 2$