Trigonometry Examples

$\frac{h}{h \sqrt{x + h} + h \sqrt{x}}$

Step 1

Factor $h$ out of $h \sqrt{x + h} + h \sqrt{x}$ .

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Step 1.1

Factor $h$ out of $h \sqrt{x + h}$ .

$\frac{h}{h (\sqrt{x + h}) + h \sqrt{x}}$

Step 1.2

Factor $h$ out of $h \sqrt{x}$ .

$\frac{h}{h (\sqrt{x + h}) + h (\sqrt{x})}$

Step 1.3

Factor $h$ out of $h (\sqrt{x + h}) + h (\sqrt{x})$ .

$\frac{h}{h (\sqrt{x + h} + \sqrt{x})}$

Step 2

Cancel the common factor of $h$ .

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Step 2.1

Cancel the common factor.

$\frac{h}{h (\sqrt{x + h} + \sqrt{x})}$

Step 2.2

Rewrite the expression.

$\frac{1}{\sqrt{x + h} + \sqrt{x}}$

Step 3

Multiply $\frac{1}{\sqrt{x + h} + \sqrt{x}}$ by $\frac{\sqrt{x + h} - \sqrt{x}}{\sqrt{x + h} - \sqrt{x}}$ .

$\frac{1}{\sqrt{x + h} + \sqrt{x}} \cdot \frac{\sqrt{x + h} - \sqrt{x}}{\sqrt{x + h} - \sqrt{x}}$

Step 4

Multiply $\frac{1}{\sqrt{x + h} + \sqrt{x}}$ by $\frac{\sqrt{x + h} - \sqrt{x}}{\sqrt{x + h} - \sqrt{x}}$ .

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

Step 5

Expand the denominator using the FOIL method.

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

Step 6

Simplify.

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Step 6.1

Add $- \sqrt{x (h + x)}$ and $\sqrt{x (h + x)}$ .

$\frac{\sqrt{x + h} - \sqrt{x}}{h + 0}$

Step 6.2

Add $h$ and $0$ .

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