Solve 1/8-1/x-16-1/14=

$$\frac { 1 } { 8 } - \frac { 1 } { x - 16 } - \frac { 1 } { 14 } =$$

Evaluate

$$\frac{3x-104}{56\left(x-16\right)}$$

Short Solution Steps

Least common multiple of 8 and 14 is 56. Convert \frac{1}{8} and \frac{1}{14} to fractions with denominator 56.

$$\frac{7}{56}-\frac{1}{x-16}-\frac{4}{56}$$

Since \frac{7}{56} and \frac{4}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-4}{56}-\frac{1}{x-16}$$

Subtract 4 from 7 to get 3.

$$\frac{3}{56}-\frac{1}{x-16}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 56 and x-16 is 56\left(x-16\right). Multiply \frac{3}{56} times \frac{x-16}{x-16}. Multiply \frac{1}{x-16} times \frac{56}{56}.

$$\frac{3\left(x-16\right)}{56\left(x-16\right)}-\frac{56}{56\left(x-16\right)}$$

Since \frac{3\left(x-16\right)}{56\left(x-16\right)} and \frac{56}{56\left(x-16\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(x-16\right)-56}{56\left(x-16\right)}$$

Do the multiplications in 3\left(x-16\right)-56.

$$\frac{3x-48-56}{56\left(x-16\right)}$$

Combine like terms in 3x-48-56.

$$\frac{3x-104}{56\left(x-16\right)}$$

Expand 56\left(x-16\right).

$$\frac{3x-104}{56x-896}$$

Factor

$$\frac{3x-104}{56\left(x-16\right)}$$