Basic Math Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Factor $h$ out of $h \sqrt{a + h} - h \sqrt{a}$ .

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Step 1.1.1

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

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

Step 1.1.2

Factor $h$ out of $- h \sqrt{a}$ .

$\frac{h}{h (\sqrt{a + h}) + h (- 1 \sqrt{a})}$

Step 1.1.3

Factor $h$ out of $h (\sqrt{a + h}) + h (- 1 \sqrt{a})$ .

$\frac{h}{h (\sqrt{a + h} - 1 \sqrt{a})}$

Step 1.2

Rewrite $- 1 \sqrt{a}$ as $- \sqrt{a}$ .

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

Step 2

Cancel the common factor of $h$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$\frac{1}{\sqrt{a + h} - \sqrt{a}}$

Step 3

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

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

Step 4

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

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

Step 5

Expand the denominator using the FOIL method.

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

Step 6

Simplify.

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Step 6.1

Subtract $a$ from $a$ .

$\frac{\sqrt{a + h} + \sqrt{a}}{h + 0}$

Step 6.2

Add $h$ and $0$ .

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