Precalculus Examples

$(\frac{4}{9}) (\frac{- \sqrt{19}}{10}) - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Factor $2$ out of $4$ .

$\frac{2 (2)}{9} \cdot \frac{- \sqrt{19}}{10} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.1.2

Factor $2$ out of $10$ .

$\frac{2 \cdot 2}{9} \cdot \frac{- \sqrt{19}}{2 \cdot 5} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.1.3

Cancel the common factor.

$\frac{2 \cdot 2}{9} \cdot \frac{- \sqrt{19}}{2 \cdot 5} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.1.4

Rewrite the expression.

$\frac{2}{9} \cdot \frac{- \sqrt{19}}{5} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.2

Multiply $\frac{2}{9}$ by $\frac{- \sqrt{19}}{5}$ .

$\frac{2 (- \sqrt{19})}{9 \cdot 5} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.3

Multiply $- 1$ by $2$ .

$\frac{- 2 \sqrt{19}}{9 \cdot 5} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.4

Multiply $9$ by $5$ .

$\frac{- 2 \sqrt{19}}{45} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.5

Move the negative in front of the fraction.

$- \frac{2 \sqrt{19}}{45} - \frac{- \sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.6

Cancel the common factor of $9$ .

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Step 1.6.1

Move the leading negative in $- \frac{- \sqrt{65}}{9}$ into the numerator.

$- \frac{2 \sqrt{19}}{45} + \frac{\sqrt{65}}{9} \cdot \frac{- 9}{10}$

Step 1.6.2

Factor $9$ out of $- 9$ .

$- \frac{2 \sqrt{19}}{45} + \frac{\sqrt{65}}{9} \cdot \frac{9 (- 1)}{10}$

Step 1.6.3

Cancel the common factor.

$- \frac{2 \sqrt{19}}{45} + \frac{\sqrt{65}}{9} \cdot \frac{9 \cdot - 1}{10}$

Step 1.6.4

Rewrite the expression.

$- \frac{2 \sqrt{19}}{45} + \sqrt{65} \cdot \frac{- 1}{10}$

Step 1.7

Combine $\sqrt{65}$ and $\frac{- 1}{10}$ .

$- \frac{2 \sqrt{19}}{45} + \frac{\sqrt{65} \cdot - 1}{10}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Move $- 1$ to the left of $\sqrt{65}$ .

$- \frac{2 \sqrt{19}}{45} + \frac{- 1 \cdot \sqrt{65}}{10}$

Step 1.8.2

Rewrite $- 1 \sqrt{65}$ as $- \sqrt{65}$ .

$- \frac{2 \sqrt{19}}{45} + \frac{- \sqrt{65}}{10}$

Step 1.9

Move the negative in front of the fraction.

$- \frac{2 \sqrt{19}}{45} - \frac{\sqrt{65}}{10}$

Step 2

To write $- \frac{2 \sqrt{19}}{45}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{2 \sqrt{19}}{45} \cdot \frac{2}{2} - \frac{\sqrt{65}}{10}$

Step 3

To write $- \frac{\sqrt{65}}{10}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{2 \sqrt{19}}{45} \cdot \frac{2}{2} - \frac{\sqrt{65}}{10} \cdot \frac{9}{9}$

Step 4

Write each expression with a common denominator of $90$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2 \sqrt{19}}{45}$ by $\frac{2}{2}$ .

$- \frac{2 \sqrt{19} \cdot 2}{45 \cdot 2} - \frac{\sqrt{65}}{10} \cdot \frac{9}{9}$

Step 4.2

Multiply $45$ by $2$ .

$- \frac{2 \sqrt{19} \cdot 2}{90} - \frac{\sqrt{65}}{10} \cdot \frac{9}{9}$

Step 4.3

Multiply $\frac{\sqrt{65}}{10}$ by $\frac{9}{9}$ .

$- \frac{2 \sqrt{19} \cdot 2}{90} - \frac{\sqrt{65} \cdot 9}{10 \cdot 9}$

Step 4.4

Multiply $10$ by $9$ .

$- \frac{2 \sqrt{19} \cdot 2}{90} - \frac{\sqrt{65} \cdot 9}{90}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 2 \sqrt{19} \cdot 2 - \sqrt{65} \cdot 9}{90}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $- 2$ .

$\frac{- 4 \sqrt{19} - \sqrt{65} \cdot 9}{90}$

Step 6.2

Multiply $9$ by $- 1$ .

$\frac{- 4 \sqrt{19} - 9 \sqrt{65}}{90}$

Step 7

Simplify with factoring out.

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Step 7.1

Factor $- 1$ out of $- 4 \sqrt{19}$ .

$\frac{- (4 \sqrt{19}) - 9 \sqrt{65}}{90}$

Step 7.2

Factor $- 1$ out of $- 9 \sqrt{65}$ .

$\frac{- (4 \sqrt{19}) - (9 \sqrt{65})}{90}$

Step 7.3

Factor $- 1$ out of $- (4 \sqrt{19}) - (9 \sqrt{65})$ .

$\frac{- (4 \sqrt{19} + 9 \sqrt{65})}{90}$

Step 7.4

Simplify the expression.

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Step 7.4.1

Rewrite $- (4 \sqrt{19} + 9 \sqrt{65})$ as $- 1 (4 \sqrt{19} + 9 \sqrt{65})$ .

$\frac{- 1 (4 \sqrt{19} + 9 \sqrt{65})}{90}$

Step 7.4.2

Move the negative in front of the fraction.

$- \frac{4 \sqrt{19} + 9 \sqrt{65}}{90}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{4 \sqrt{19} + 9 \sqrt{65}}{90}$

Decimal Form:

$- 0.99995461 \dots$