Calculus Examples

$\frac{1}{6 x^{2}} - \frac{6}{x}$

Step 1

To write $- \frac{6}{x}$ as a fraction with a common denominator, multiply by $\frac{6 x}{6 x}$ .

$\frac{1}{6 x^{2}} - \frac{6}{x} \cdot \frac{6 x}{6 x}$

Step 2

Write each expression with a common denominator of $6 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{6}{x}$ by $\frac{6 x}{6 x}$ .

$\frac{1}{6 x^{2}} - \frac{6 (6 x)}{x (6 x)}$

Step 2.2

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

$\frac{1}{6 x^{2}} - \frac{6 (6 x)}{6 (x^{1} x)}$

Step 2.3

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

$\frac{1}{6 x^{2}} - \frac{6 (6 x)}{6 (x^{1} x^{1})}$

Step 2.4

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

$\frac{1}{6 x^{2}} - \frac{6 (6 x)}{6 x^{1 + 1}}$

Step 2.5

Add $1$ and $1$ .

$\frac{1}{6 x^{2}} - \frac{6 (6 x)}{6 x^{2}}$

Step 3

Combine the numerators over the common denominator.

$\frac{1 - 6 (6 x)}{6 x^{2}}$

Step 4

Multiply $- 6$ by $6$ .

$\frac{1 - 36 x}{6 x^{2}}$