Trigonometry Examples

$\frac{\frac{5 \sqrt{34}}{34}}{- \frac{3 \sqrt{34}}{34}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 \sqrt{34}}{34} (- \frac{34}{3 \sqrt{34}})$

Step 2

Cancel the common factor of $\sqrt{34}$ .

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Step 2.1

Move the leading negative in $- \frac{34}{3 \sqrt{34}}$ into the numerator.

$\frac{5 \sqrt{34}}{34} \cdot \frac{- 34}{3 \sqrt{34}}$

Step 2.2

Factor $\sqrt{34}$ out of $5 \sqrt{34}$ .

$\frac{\sqrt{34} \cdot 5}{34} \cdot \frac{- 34}{3 \sqrt{34}}$

Step 2.3

Factor $\sqrt{34}$ out of $3 \sqrt{34}$ .

$\frac{\sqrt{34} \cdot 5}{34} \cdot \frac{- 34}{\sqrt{34} \cdot 3}$

Step 2.4

Cancel the common factor.

$\frac{\sqrt{34} \cdot 5}{34} \cdot \frac{- 34}{\sqrt{34} \cdot 3}$

Step 2.5

Rewrite the expression.

$\frac{5}{34} \cdot \frac{- 34}{3}$

Step 3

Cancel the common factor of $34$ .

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Step 3.1

Factor $34$ out of $- 34$ .

$\frac{5}{34} \cdot \frac{34 (- 1)}{3}$

Step 3.2

Cancel the common factor.

$\frac{5}{34} \cdot \frac{34 \cdot - 1}{3}$

Step 3.3

Rewrite the expression.

$5 (\frac{- 1}{3})$

Step 4

Combine $5$ and $\frac{- 1}{3}$ .

$\frac{5 \cdot - 1}{3}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $5$ by $- 1$ .

$\frac{- 5}{3}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{5}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{3}$

Decimal Form:

$- 1.\overline{6}$

Mixed Number Form:

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