Precalculus Examples

$- \frac{20}{29} \cdot (- \frac{\sqrt{119}}{12}) + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $4$ .

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Step 1.1.1

Move the leading negative in $- \frac{20}{29}$ into the numerator.

$\frac{- 20}{29} \cdot (- \frac{\sqrt{119}}{12}) + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.1.2

Move the leading negative in $- \frac{\sqrt{119}}{12}$ into the numerator.

$\frac{- 20}{29} \cdot \frac{- \sqrt{119}}{12} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.1.3

Factor $4$ out of $- 20$ .

$\frac{4 (- 5)}{29} \cdot \frac{- \sqrt{119}}{12} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.1.4

Factor $4$ out of $12$ .

$\frac{4 \cdot - 5}{29} \cdot \frac{- \sqrt{119}}{4 \cdot 3} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.1.5

Cancel the common factor.

$\frac{4 \cdot - 5}{29} \cdot \frac{- \sqrt{119}}{4 \cdot 3} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.1.6

Rewrite the expression.

$\frac{- 5}{29} \cdot \frac{- \sqrt{119}}{3} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.2

Multiply $\frac{- 5}{29}$ by $\frac{- \sqrt{119}}{3}$ .

$\frac{- 5 (- \sqrt{119})}{29 \cdot 3} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.3

Multiply $- 1$ by $- 5$ .

$\frac{5 \sqrt{119}}{29 \cdot 3} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.4

Multiply $29$ by $3$ .

$\frac{5 \sqrt{119}}{87} + \frac{21}{29} \cdot (- \frac{5}{12})$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Move the leading negative in $- \frac{5}{12}$ into the numerator.

$\frac{5 \sqrt{119}}{87} + \frac{21}{29} \cdot \frac{- 5}{12}$

Step 1.5.2

Factor $3$ out of $21$ .

$\frac{5 \sqrt{119}}{87} + \frac{3 (7)}{29} \cdot \frac{- 5}{12}$

Step 1.5.3

Factor $3$ out of $12$ .

$\frac{5 \sqrt{119}}{87} + \frac{3 \cdot 7}{29} \cdot \frac{- 5}{3 \cdot 4}$

Step 1.5.4

Cancel the common factor.

$\frac{5 \sqrt{119}}{87} + \frac{3 \cdot 7}{29} \cdot \frac{- 5}{3 \cdot 4}$

Step 1.5.5

Rewrite the expression.

$\frac{5 \sqrt{119}}{87} + \frac{7}{29} \cdot \frac{- 5}{4}$

Step 1.6

Multiply $\frac{7}{29}$ by $\frac{- 5}{4}$ .

$\frac{5 \sqrt{119}}{87} + \frac{7 \cdot - 5}{29 \cdot 4}$

Step 1.7

Multiply $7$ by $- 5$ .

$\frac{5 \sqrt{119}}{87} + \frac{- 35}{29 \cdot 4}$

Step 1.8

Multiply $29$ by $4$ .

$\frac{5 \sqrt{119}}{87} + \frac{- 35}{116}$

Step 1.9

Move the negative in front of the fraction.

$\frac{5 \sqrt{119}}{87} - \frac{35}{116}$

Step 2

To write $\frac{5 \sqrt{119}}{87}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 \sqrt{119}}{87} \cdot \frac{4}{4} - \frac{35}{116}$

Step 3

To write $- \frac{35}{116}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 \sqrt{119}}{87} \cdot \frac{4}{4} - \frac{35}{116} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $348$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5 \sqrt{119}}{87}$ by $\frac{4}{4}$ .

$\frac{5 \sqrt{119} \cdot 4}{87 \cdot 4} - \frac{35}{116} \cdot \frac{3}{3}$

Step 4.2

Multiply $87$ by $4$ .

$\frac{5 \sqrt{119} \cdot 4}{348} - \frac{35}{116} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{35}{116}$ by $\frac{3}{3}$ .

$\frac{5 \sqrt{119} \cdot 4}{348} - \frac{35 \cdot 3}{116 \cdot 3}$

Step 4.4

Multiply $116$ by $3$ .

$\frac{5 \sqrt{119} \cdot 4}{348} - \frac{35 \cdot 3}{348}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \sqrt{119} \cdot 4 - 35 \cdot 3}{348}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $5$ .

$\frac{20 \sqrt{119} - 35 \cdot 3}{348}$

Step 6.2

Multiply $- 35$ by $3$ .

$\frac{20 \sqrt{119} - 105}{348}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{20 \sqrt{119} - 105}{348}$

Decimal Form:

$0.32521333 \dots$