Finite Math Examples

$\frac{3 (\sqrt{7} - \sqrt{5})}{(\sqrt{7} + \sqrt{5}) (\sqrt{7} - \sqrt{5})}$

Step 1

Cancel the common factor of $\sqrt{7} - \sqrt{5}$ .

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Step 1.1

Cancel the common factor.

$\frac{3 (\sqrt{7} - \sqrt{5})}{(\sqrt{7} + \sqrt{5}) (\sqrt{7} - \sqrt{5})}$

Step 1.2

Rewrite the expression.

$\frac{3}{\sqrt{7} + \sqrt{5}}$

Step 2

Multiply $\frac{3}{\sqrt{7} + \sqrt{5}}$ by $\frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} - \sqrt{5}}$ .

$\frac{3}{\sqrt{7} + \sqrt{5}} \cdot \frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} - \sqrt{5}}$

Step 3

Multiply $\frac{3}{\sqrt{7} + \sqrt{5}}$ by $\frac{\sqrt{7} - \sqrt{5}}{\sqrt{7} - \sqrt{5}}$ .

$\frac{3 (\sqrt{7} - \sqrt{5})}{(\sqrt{7} + \sqrt{5}) (\sqrt{7} - \sqrt{5})}$

Step 4

Expand the denominator using the FOIL method.

$\frac{3 (\sqrt{7} - \sqrt{5})}{{\sqrt{7}}^{2} - \sqrt{35} + \sqrt{35} - {\sqrt{5}}^{2}}$

Step 5

Simplify.

$\frac{3 (\sqrt{7} - \sqrt{5})}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (\sqrt{7} - \sqrt{5})}{2}$

Decimal Form:

$0.61452500 \dots$