Linear Algebra Examples

$\frac{- 9}{8 + 5 \sqrt{7}}$

Step 1

Move the negative in front of the fraction.

$- \frac{9}{8 + 5 \sqrt{7}}$

Step 2

Multiply $\frac{9}{8 + 5 \sqrt{7}}$ by $\frac{8 - 5 \sqrt{7}}{8 - 5 \sqrt{7}}$ .

$- (\frac{9}{8 + 5 \sqrt{7}} \cdot \frac{8 - 5 \sqrt{7}}{8 - 5 \sqrt{7}})$

Step 3

Multiply $\frac{9}{8 + 5 \sqrt{7}}$ by $\frac{8 - 5 \sqrt{7}}{8 - 5 \sqrt{7}}$ .

$- \frac{9 (8 - 5 \sqrt{7})}{(8 + 5 \sqrt{7}) (8 - 5 \sqrt{7})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{9 (8 - 5 \sqrt{7})}{64 - 40 \sqrt{7} + 40 \sqrt{7} - 25 {\sqrt{7}}^{2}}$

Step 5

Simplify.

$- \frac{9 (8 - 5 \sqrt{7})}{- 111}$

Step 6

Cancel the common factor of $9$ and $- 111$ .

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Step 6.1

Factor $3$ out of $9 (8 - 5 \sqrt{7})$ .

$- \frac{3 (3 (8 - 5 \sqrt{7}))}{- 111}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $- 111$ .

$- \frac{3 (3 (8 - 5 \sqrt{7}))}{3 (- 37)}$

Step 6.2.2

Cancel the common factor.

$- \frac{3 (3 (8 - 5 \sqrt{7}))}{3 \cdot - 37}$

Step 6.2.3

Rewrite the expression.

$- \frac{3 (8 - 5 \sqrt{7})}{- 37}$

Step 7

Move the negative in front of the fraction.

$- - \frac{3 (8 - 5 \sqrt{7})}{37}$

Step 8

Multiply $- - \frac{3 (8 - 5 \sqrt{7})}{37}$ .

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Step 8.1

Multiply $- 1$ by $- 1$ .

$1 \frac{3 (8 - 5 \sqrt{7})}{37}$

Step 8.2

Multiply $\frac{3 (8 - 5 \sqrt{7})}{37}$ by $1$ .

$\frac{3 (8 - 5 \sqrt{7})}{37}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (8 - 5 \sqrt{7})}{37}$

Decimal Form:

$- 0.42395323 \dots$