Simplify (8x-6)/(7x-42)-x/(x-6)

$\frac{8 x - 6}{7 x - 42} - \frac{x}{x - 6}$

Step 1

Simplify each term.

Factor $2$ out of $8 x - 6$ .

Factor $2$ out of $8 x$ .

$\frac{2 (4 x) - 6}{7 x - 42} - \frac{x}{x - 6}$

Factor $2$ out of $- 6$ .

$\frac{2 (4 x) + 2 (- 3)}{7 x - 42} - \frac{x}{x - 6}$

Factor $2$ out of $2 (4 x) + 2 (- 3)$ .

$\frac{2 (4 x - 3)}{7 x - 42} - \frac{x}{x - 6}$

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

Factor $7$ out of $7 x$ .

$\frac{2 (4 x - 3)}{7 (x) - 42} - \frac{x}{x - 6}$

Factor $7$ out of $- 42$ .

$\frac{2 (4 x - 3)}{7 x + 7 \cdot - 6} - \frac{x}{x - 6}$

Factor $7$ out of $7 x + 7 \cdot - 6$ .

$\frac{2 (4 x - 3)}{7 (x - 6)} - \frac{x}{x - 6}$

Step 2

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

$\frac{2 (4 x - 3)}{7 (x - 6)} - \frac{x}{x - 6} \cdot \frac{7}{7}$

Step 3

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

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

$\frac{2 (4 x - 3)}{7 (x - 6)} - \frac{x \cdot 7}{(x - 6) \cdot 7}$

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

$\frac{2 (4 x - 3)}{7 (x - 6)} - \frac{x \cdot 7}{7 (x - 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 (4 x - 3) - x \cdot 7}{7 (x - 6)}$

Step 5

Simplify the numerator.

Apply the distributive property.

$\frac{2 (4 x) + 2 \cdot - 3 - x \cdot 7}{7 (x - 6)}$

Multiply $4$ by $2$ .

$\frac{8 x + 2 \cdot - 3 - x \cdot 7}{7 (x - 6)}$

Multiply $2$ by $- 3$ .

$\frac{8 x - 6 - x \cdot 7}{7 (x - 6)}$

Multiply $7$ by $- 1$ .

$\frac{8 x - 6 - 7 x}{7 (x - 6)}$

Subtract $7 x$ from $8 x$ .

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

Step 6

Cancel the common factor of $x - 6$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$

Simplify (8x-6)/(7x-42)-x/(x-6)

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