Trigonometry Examples

$\frac{- 8 x^{3}}{\sqrt{- 9 x + 3}}$

Step 1

Factor $3$ out of $- 9 x + 3$ .

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Step 1.1

Factor $3$ out of $- 9 x$ .

$\frac{- 8 x^{3}}{\sqrt{3 (- 3 x) + 3}}$

Step 1.2

Factor $3$ out of $3$ .

$\frac{- 8 x^{3}}{\sqrt{3 (- 3 x) + 3 (1)}}$

Step 1.3

Factor $3$ out of $3 (- 3 x) + 3 (1)$ .

$\frac{- 8 x^{3}}{\sqrt{3 (- 3 x + 1)}}$

Step 2

Move the negative in front of the fraction.

$- \frac{8 x^{3}}{\sqrt{3 (- 3 x + 1)}}$

Step 3

Multiply $\frac{8 x^{3}}{\sqrt{3 (- 3 x + 1)}}$ by $\frac{\sqrt{3 (- 3 x + 1)}}{\sqrt{3 (- 3 x + 1)}}$ .

$- (\frac{8 x^{3}}{\sqrt{3 (- 3 x + 1)}} \cdot \frac{\sqrt{3 (- 3 x + 1)}}{\sqrt{3 (- 3 x + 1)}})$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{8 x^{3}}{\sqrt{3 (- 3 x + 1)}}$ by $\frac{\sqrt{3 (- 3 x + 1)}}{\sqrt{3 (- 3 x + 1)}}$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{\sqrt{3 (- 3 x + 1)} \sqrt{3 (- 3 x + 1)}}$

Step 4.2

Raise $\sqrt{3 (- 3 x + 1)}$ to the power of $1$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{\sqrt{3 (- 3 x + 1)}}^{1} \sqrt{3 (- 3 x + 1)}}$

Step 4.3

Raise $\sqrt{3 (- 3 x + 1)}$ to the power of $1$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{\sqrt{3 (- 3 x + 1)}}^{1} {\sqrt{3 (- 3 x + 1)}}^{1}}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{\sqrt{3 (- 3 x + 1)}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{\sqrt{3 (- 3 x + 1)}}^{2}}$

Step 4.6

Rewrite ${\sqrt{3 (- 3 x + 1)}}^{2}$ as $3 (- 3 x + 1)$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 (- 3 x + 1)}$ as ${(3 (- 3 x + 1))}^{\frac{1}{2}}$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{({(3 (- 3 x + 1))}^{\frac{1}{2}})}^{2}}$

Step 4.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{(3 (- 3 x + 1))}^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

Combine $\frac{1}{2}$ and $2$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{(3 (- 3 x + 1))}^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{(3 (- 3 x + 1))}^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{{(3 (- 3 x + 1))}^{1}}$

Step 4.6.5

Simplify.

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (- 3 x + 1)}$

Step 5

Factor $- 1$ out of $- 3 x$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (- (3 x) + 1)}$

Step 6

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

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (- (3 x) - 1 (- 1))}$

Step 7

Factor $- 1$ out of $- (3 x) - 1 (- 1)$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (- (3 x - 1))}$

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (3 x - 1)$ as $- 1 (3 x - 1)$ .

$- \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (- 1 (3 x - 1))}$

Step 8.2

Move the negative in front of the fraction.

$- - \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (3 x - 1)}$

Step 8.3

Multiply $- 1$ by $- 1$ .

$1 \frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (3 x - 1)}$

Step 8.4

Multiply $\frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (3 x - 1)}$ by $1$ .

$\frac{8 x^{3} \sqrt{3 (- 3 x + 1)}}{3 (3 x - 1)}$