Basic Math Examples

\frac{- 9}{4 \sqrt{2} + 2}

$\frac{- 9}{4 \sqrt{2} + 2}$

Step 1

Move the negative in front of the fraction.

- \frac{9}{4 \sqrt{2} + 2}

$- \frac{9}{4 \sqrt{2} + 2}$

Step 2

Multiply

\frac{9}{4 \sqrt{2} + 2}

$\frac{9}{4 \sqrt{2} + 2}$ by

\frac{4 \sqrt{2} - 2}{4 \sqrt{2} - 2}

$\frac{4 \sqrt{2} - 2}{4 \sqrt{2} - 2}$ .

- (\frac{9}{4 \sqrt{2} + 2} \cdot \frac{4 \sqrt{2} - 2}{4 \sqrt{2} - 2})

$- (\frac{9}{4 \sqrt{2} + 2} \cdot \frac{4 \sqrt{2} - 2}{4 \sqrt{2} - 2})$

Step 3

Multiply

\frac{9}{4 \sqrt{2} + 2}

$\frac{9}{4 \sqrt{2} + 2}$ by

\frac{4 \sqrt{2} - 2}{4 \sqrt{2} - 2}

$\frac{4 \sqrt{2} - 2}{4 \sqrt{2} - 2}$ .

- \frac{9 (4 \sqrt{2} - 2)}{(4 \sqrt{2} + 2) (4 \sqrt{2} - 2)}

$- \frac{9 (4 \sqrt{2} - 2)}{(4 \sqrt{2} + 2) (4 \sqrt{2} - 2)}$

Step 4

Expand the denominator using the FOIL method.

- \frac{9 (4 \sqrt{2} - 2)}{16 {\sqrt{2}}^{2} - 8 \sqrt{2} + 8 \sqrt{2} - 4}

$- \frac{9 (4 \sqrt{2} - 2)}{16 {\sqrt{2}}^{2} - 8 \sqrt{2} + 8 \sqrt{2} - 4}$

Step 5

Simplify.

- \frac{9 (4 \sqrt{2} - 2)}{28}

$- \frac{9 (4 \sqrt{2} - 2)}{28}$

Step 6

Cancel the common factor of

4 \sqrt{2} - 2

$4 \sqrt{2} - 2$ and

28

$28$ .

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Step 6.1

Factor

2

$2$ out of

9 (4 \sqrt{2} - 2)

$9 (4 \sqrt{2} - 2)$ .

- \frac{2 (9 (2 \sqrt{2} - 1))}{28}

$- \frac{2 (9 (2 \sqrt{2} - 1))}{28}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor

2

$2$ out of

28

$28$ .

- \frac{2 (9 (2 \sqrt{2} - 1))}{2 (14)}

$- \frac{2 (9 (2 \sqrt{2} - 1))}{2 (14)}$

Step 6.2.2

Cancel the common factor.

$- \frac{2 (9 (2 \sqrt{2} - 1))}{2 \cdot 14}$

Step 6.2.3

Rewrite the expression.

$- \frac{9 (2 \sqrt{2} - 1)}{14}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{9 (2 \sqrt{2} - 1)}{14}$

Decimal Form:

$- 1.17541743 \dots$