Trigonometry Examples

$\frac{x^{- 1} y^{4}}{3 x^{- 5} y - 1}$

Step 1

Move $x^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{4}}{(3 x^{- 5} y - 1) x}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{y^{4}}{(3 \frac{1}{x^{5}} y - 1) x}$

Step 2.2

Combine $3$ and $\frac{1}{x^{5}}$ .

$\frac{y^{4}}{(\frac{3}{x^{5}} y - 1) x}$

Step 2.3

Combine $\frac{3}{x^{5}}$ and $y$ .

$\frac{y^{4}}{(\frac{3 y}{x^{5}} - 1) x}$

Step 2.4

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{x^{5}}{x^{5}}$ .

$\frac{y^{4}}{(\frac{3 y}{x^{5}} - 1 \cdot \frac{x^{5}}{x^{5}}) x}$

Step 2.5

Combine $- 1$ and $\frac{x^{5}}{x^{5}}$ .

$\frac{y^{4}}{(\frac{3 y}{x^{5}} + \frac{- x^{5}}{x^{5}}) x}$

Step 2.6

Combine the numerators over the common denominator.

$\frac{y^{4}}{\frac{3 y - x^{5}}{x^{5}} x}$

Step 3

Simplify terms.

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Step 3.1

Combine $\frac{3 y - x^{5}}{x^{5}}$ and $x$ .

$\frac{y^{4}}{\frac{(3 y - x^{5}) x}{x^{5}}}$

Step 3.2

Reduce the expression $\frac{(3 y - x^{5}) x}{x^{5}}$ by cancelling the common factors.

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Step 3.2.1

Factor $x$ out of $(3 y - x^{5}) x$ .

$\frac{y^{4}}{\frac{x (3 y - x^{5})}{x^{5}}}$

Step 3.2.2

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

$\frac{y^{4}}{\frac{x (3 y - x^{5})}{x \cdot x^{4}}}$

Step 3.2.3

Cancel the common factor.

$\frac{y^{4}}{\frac{x (3 y - x^{5})}{x \cdot x^{4}}}$

Step 3.2.4

Rewrite the expression.

$\frac{y^{4}}{\frac{3 y - x^{5}}{x^{4}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$y^{4} \frac{x^{4}}{3 y - x^{5}}$

Step 5

Combine $y^{4}$ and $\frac{x^{4}}{3 y - x^{5}}$ .

$\frac{y^{4} x^{4}}{3 y - x^{5}}$