Pre-Algebra Examples

$\frac{7}{x} - 6 \div \frac{7 - 6 x}{7}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{x} - (6 \frac{7}{7 - 6 x})$

Step 1.2

Multiply $6 \frac{7}{7 - 6 x}$ .

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Step 1.2.1

Combine $6$ and $\frac{7}{7 - 6 x}$ .

$\frac{7}{x} - \frac{6 \cdot 7}{7 - 6 x}$

Step 1.2.2

Multiply $6$ by $7$ .

$\frac{7}{x} - \frac{42}{7 - 6 x}$

Step 2

To write $\frac{7}{x}$ as a fraction with a common denominator, multiply by $\frac{7 - 6 x}{7 - 6 x}$ .

$\frac{7}{x} \cdot \frac{7 - 6 x}{7 - 6 x} - \frac{42}{7 - 6 x}$

Step 3

To write $- \frac{42}{7 - 6 x}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{7}{x} \cdot \frac{7 - 6 x}{7 - 6 x} - \frac{42}{7 - 6 x} \cdot \frac{x}{x}$

Step 4

Write each expression with a common denominator of $x (7 - 6 x)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{x}$ by $\frac{7 - 6 x}{7 - 6 x}$ .

$\frac{7 (7 - 6 x)}{x (7 - 6 x)} - \frac{42}{7 - 6 x} \cdot \frac{x}{x}$

Step 4.2

Multiply $\frac{42}{7 - 6 x}$ by $\frac{x}{x}$ .

$\frac{7 (7 - 6 x)}{x (7 - 6 x)} - \frac{42 x}{(7 - 6 x) x}$

Step 4.3

Reorder the factors of $(7 - 6 x) x$ .

$\frac{7 (7 - 6 x)}{x (7 - 6 x)} - \frac{42 x}{x (7 - 6 x)}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 (7 - 6 x) - 42 x}{x (7 - 6 x)}$

Step 6

Simplify the numerator.

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Step 6.1

Factor $7$ out of $7 (7 - 6 x) - 42 x$ .

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Step 6.1.1

Factor $7$ out of $- 42 x$ .

$\frac{7 (7 - 6 x) + 7 (- 6 x)}{x (7 - 6 x)}$

Step 6.1.2

Factor $7$ out of $7 (7 - 6 x) + 7 (- 6 x)$ .

$\frac{7 (7 - 6 x - 6 x)}{x (7 - 6 x)}$

Step 6.2

Subtract $6 x$ from $- 6 x$ .

$\frac{7 (7 - 12 x)}{x (7 - 6 x)}$