Trigonometry Examples

$\frac{- 27 x^{5} + 60 x^{6}}{15 x^{6}}$

Step 1

Factor $3 x^{5}$ out of $- 27 x^{5} + 60 x^{6}$ .

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Step 1.1

Factor $3 x^{5}$ out of $- 27 x^{5}$ .

$\frac{3 x^{5} (- 9) + 60 x^{6}}{15 x^{6}}$

Step 1.2

Factor $3 x^{5}$ out of $60 x^{6}$ .

$\frac{3 x^{5} (- 9) + 3 x^{5} (20 x)}{15 x^{6}}$

Step 1.3

Factor $3 x^{5}$ out of $3 x^{5} (- 9) + 3 x^{5} (20 x)$ .

$\frac{3 x^{5} (- 9 + 20 x)}{15 x^{6}}$

$\frac{3 x^{5} (- 9 + 20 x)}{15 x^{6}}$

Step 2

Cancel the common factor of $3$ and $15$ .

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Step 2.1

Factor $3$ out of $3 x^{5} (- 9 + 20 x)$ .

$\frac{3 (x^{5} (- 9 + 20 x))}{15 x^{6}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $15 x^{6}$ .

$\frac{3 (x^{5} (- 9 + 20 x))}{3 (5 x^{6})}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (x^{5} (- 9 + 20 x))}{3 (5 x^{6})}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{5} (- 9 + 20 x)}{5 x^{6}}$

$\frac{x^{5} (- 9 + 20 x)}{5 x^{6}}$

$\frac{x^{5} (- 9 + 20 x)}{5 x^{6}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor $x^{5}$ out of $5 x^{6}$ .

$\frac{x^{5} (- 9 + 20 x)}{x^{5} (5 x)}$

Step 3.2

Cancel the common factor.

$\frac{x^{5} (- 9 + 20 x)}{x^{5} (5 x)}$

Step 3.3

Rewrite the expression.

$\frac{- 9 + 20 x}{5 x}$

$\frac{- 9 + 20 x}{5 x}$

Step 4

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- 1 (9) + 20 x}{5 x}$

Step 5

Factor $- 1$ out of $20 x$ .

$\frac{- 1 (9) - (- 20 x)}{5 x}$

Step 6

Factor $- 1$ out of $- 1 (9) - (- 20 x)$ .

$\frac{- 1 (9 - 20 x)}{5 x}$

Step 7

Move the negative in front of the fraction.

$- \frac{9 - 20 x}{5 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$