Precalculus Examples

$\frac{- 3 e^{- 3 \ln (x)}}{x}$

Step 1

Simplify the numerator.

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Step 1.1

Simplify $- 3 \ln (x)$ by moving $- 3$ inside the logarithm.

$\frac{- 3 e^{\ln (x^{- 3})}}{x}$

Step 1.2

Exponentiation and log are inverse functions.

$\frac{- 3 x^{- 3}}{x}$

Step 1.3

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

$\frac{- 3 \frac{1}{x^{3}}}{x}$

Step 2

Combine fractions.

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Step 2.1

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

$\frac{\frac{- 3}{x^{3}}}{x}$

Step 2.2

Move the negative in front of the fraction.

$\frac{- \frac{3}{x^{3}}}{x}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{3}{x^{3}} \cdot \frac{1}{x}$

Step 4

Multiply $- \frac{3}{x^{3}} \cdot \frac{1}{x}$ .

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Step 4.1

Multiply $\frac{1}{x}$ by $\frac{3}{x^{3}}$ .

$- \frac{3}{x \cdot x^{3}}$

Step 4.2

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 4.2.1

Multiply $x$ by $x^{3}$ .

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Step 4.2.1.1

Raise $x$ to the power of $1$ .

$- \frac{3}{x^{1} x^{3}}$

Step 4.2.1.2

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

$- \frac{3}{x^{1 + 3}}$

Step 4.2.2

Add $1$ and $3$ .

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