Solve x/6x-7-x-1/8x

$$\frac { x } { 6 x - 7 } - \frac { x - 1 } { 8 x }$$

Evaluate

$$\frac{\left(2x-1\right)\left(x+7\right)}{8x\left(6x-7\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6x-7 and 8x is 8x\left(6x-7\right). Multiply \frac{x}{6x-7} times \frac{8x}{8x}. Multiply \frac{x-1}{8x} times \frac{6x-7}{6x-7}.

$$\frac{x\times 8x}{8x\left(6x-7\right)}-\frac{\left(x-1\right)\left(6x-7\right)}{8x\left(6x-7\right)}$$

Since \frac{x\times 8x}{8x\left(6x-7\right)} and \frac{\left(x-1\right)\left(6x-7\right)}{8x\left(6x-7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 8x-\left(x-1\right)\left(6x-7\right)}{8x\left(6x-7\right)}$$

Do the multiplications in x\times 8x-\left(x-1\right)\left(6x-7\right).

$$\frac{8x^{2}-6x^{2}+7x+6x-7}{8x\left(6x-7\right)}$$

Combine like terms in 8x^{2}-6x^{2}+7x+6x-7.

$$\frac{2x^{2}+13x-7}{8x\left(6x-7\right)}$$

Expand 8x\left(6x-7\right).

$$\frac{2x^{2}+13x-7}{48x^{2}-56x}$$

Expand

$$\frac{2x^{2}+13x-7}{8x\left(6x-7\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6x-7 and 8x is 8x\left(6x-7\right). Multiply \frac{x}{6x-7} times \frac{8x}{8x}. Multiply \frac{x-1}{8x} times \frac{6x-7}{6x-7}.

$$\frac{x\times 8x}{8x\left(6x-7\right)}-\frac{\left(x-1\right)\left(6x-7\right)}{8x\left(6x-7\right)}$$

Since \frac{x\times 8x}{8x\left(6x-7\right)} and \frac{\left(x-1\right)\left(6x-7\right)}{8x\left(6x-7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times 8x-\left(x-1\right)\left(6x-7\right)}{8x\left(6x-7\right)}$$

Do the multiplications in x\times 8x-\left(x-1\right)\left(6x-7\right).

$$\frac{8x^{2}-6x^{2}+7x+6x-7}{8x\left(6x-7\right)}$$

Combine like terms in 8x^{2}-6x^{2}+7x+6x-7.

$$\frac{2x^{2}+13x-7}{8x\left(6x-7\right)}$$

Expand 8x\left(6x-7\right).

$$\frac{2x^{2}+13x-7}{48x^{2}-56x}$$