Algebra Examples

$\frac{\sqrt{7}}{\sqrt{3} - \sqrt{2}}$

Step 1

Multiply $\frac{\sqrt{7}}{\sqrt{3} - \sqrt{2}}$ by $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ .

$\frac{\sqrt{7}}{\sqrt{3} - \sqrt{2}} \cdot \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$

Step 2

Multiply $\frac{\sqrt{7}}{\sqrt{3} - \sqrt{2}}$ by $\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ .

$\frac{\sqrt{7} (\sqrt{3} + \sqrt{2})}{(\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{7} (\sqrt{3} + \sqrt{2})}{{\sqrt{3}}^{2} + \sqrt{6} - \sqrt{6} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

$\frac{\sqrt{7} (\sqrt{3} + \sqrt{2})}{1}$

Step 5

Divide $\sqrt{7} (\sqrt{3} + \sqrt{2})$ by $1$ .

$\sqrt{7} (\sqrt{3} + \sqrt{2})$

Step 6

Apply the distributive property.

$\sqrt{7} \sqrt{3} + \sqrt{7} \sqrt{2}$

Step 7

Combine using the product rule for radicals.

$\sqrt{7 \cdot 3} + \sqrt{7} \sqrt{2}$

Step 8

Combine using the product rule for radicals.

$\sqrt{7 \cdot 3} + \sqrt{7 \cdot 2}$

Step 9

Simplify each term.

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Step 9.1

Multiply $7$ by $3$ .

$\sqrt{21} + \sqrt{7 \cdot 2}$

Step 9.2

Multiply $7$ by $2$ .

$\sqrt{21} + \sqrt{14}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\sqrt{21} + \sqrt{14}$

Decimal Form:

$8.32423308 \dots$