Finite Math Examples

$\frac{3}{1 - \sqrt{2}}$

Step 1

Multiply $\frac{3}{1 - \sqrt{2}}$ by $\frac{1 + \sqrt{2}}{1 + \sqrt{2}}$ .

$\frac{3}{1 - \sqrt{2}} \cdot \frac{1 + \sqrt{2}}{1 + \sqrt{2}}$

Step 2

Multiply $\frac{3}{1 - \sqrt{2}}$ by $\frac{1 + \sqrt{2}}{1 + \sqrt{2}}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Simplify the expression.

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Step 5.1

Move the negative one from the denominator of $\frac{3 (1 + \sqrt{2})}{- 1}$ .

$- 1 \cdot (3 (1 + \sqrt{2}))$

Step 5.2

Rewrite $- 1 \cdot (3 (1 + \sqrt{2}))$ as $- (3 (1 + \sqrt{2}))$ .

$- (3 (1 + \sqrt{2}))$

Step 6

Apply the distributive property.

$- (3 \cdot 1 + 3 \sqrt{2})$

Step 7

Multiply $3$ by $1$ .

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

Step 8

Apply the distributive property.

$- 1 \cdot 3 - (3 \sqrt{2})$

Step 9

Multiply.

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Step 9.1

Multiply $- 1$ by $3$ .

$- 3 - (3 \sqrt{2})$

Step 9.2

Multiply $3$ by $- 1$ .

$- 3 - 3 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- 3 - 3 \sqrt{2}$

Decimal Form:

$- 7.24264068 \dots$