Solve 8x-6/7x-42-x/x-6

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

Evaluate

$$\frac{1}{7}\approx 0.142857143$$

Short Solution Steps

Factor 7x-42.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7\left(x-6\right) and x-6 is 7\left(x-6\right). Multiply \frac{x}{x-6} times \frac{7}{7}.

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

Since \frac{8x-6}{7\left(x-6\right)} and \frac{7x}{7\left(x-6\right)} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in 8x-6-7x.

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

Cancel out x-6 in both numerator and denominator.

$$\frac{1}{7}$$

Factor

$$\frac{1}{7} = 0.14285714285714285$$