Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $x$ .

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Step 1.1.1

Move the leading negative in $- \frac{1}{x^{2}}$ into the numerator.

$\frac{1}{36} + \frac{- 1}{x^{2}} \cdot (6 x)$

Step 1.1.2

Factor $x$ out of $x^{2}$ .

$\frac{1}{36} + \frac{- 1}{x \cdot x} \cdot (6 x)$

Step 1.1.3

Factor $x$ out of $6 x$ .

$\frac{1}{36} + \frac{- 1}{x \cdot x} \cdot (x \cdot 6)$

Step 1.1.4

Cancel the common factor.

$\frac{1}{36} + \frac{- 1}{x \cdot x} \cdot (x \cdot 6)$

Step 1.1.5

Rewrite the expression.

$\frac{1}{36} + \frac{- 1}{x} \cdot 6$

Step 1.2

Combine $\frac{- 1}{x}$ and $6$ .

$\frac{1}{36} + \frac{- 1 \cdot 6}{x}$

Step 1.3

Multiply $- 1$ by $6$ .

$\frac{1}{36} + \frac{- 6}{x}$

Step 1.4

Move the negative in front of the fraction.

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

Step 2

To write $\frac{1}{36}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{36} \cdot \frac{x}{x} - \frac{6}{x}$

Step 3

To write $- \frac{6}{x}$ as a fraction with a common denominator, multiply by $\frac{36}{36}$ .

$\frac{1}{36} \cdot \frac{x}{x} - \frac{6}{x} \cdot \frac{36}{36}$

Step 4

Write each expression with a common denominator of $36 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{36}$ by $\frac{x}{x}$ .

$\frac{x}{36 x} - \frac{6}{x} \cdot \frac{36}{36}$

Step 4.2

Multiply $\frac{6}{x}$ by $\frac{36}{36}$ .

$\frac{x}{36 x} - \frac{6 \cdot 36}{x \cdot 36}$

Step 4.3

Reorder the factors of $x \cdot 36$ .

$\frac{x}{36 x} - \frac{6 \cdot 36}{36 x}$

Step 5

Combine the numerators over the common denominator.

$\frac{x - 6 \cdot 36}{36 x}$

Step 6

Multiply $- 6$ by $36$ .

$\frac{x - 216}{36 x}$