Solve x+12x/8x-x-8/3x

$$\frac{ x+12x }{ 8x } - \frac{ x-8 }{ 3x }$$

Evaluate

$$\frac{31}{24}+\frac{8}{3x}$$

Short Solution Steps

Combine x and 12x to get 13x.

$$\frac{13x}{8x}-\frac{x-8}{3x}$$

Cancel out x in both numerator and denominator.

$$\frac{13}{8}-\frac{x-8}{3x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 3x is 24x. Multiply \frac{13}{8} times \frac{3x}{3x}. Multiply \frac{x-8}{3x} times \frac{8}{8}.

$$\frac{13\times 3x}{24x}-\frac{8\left(x-8\right)}{24x}$$

Since \frac{13\times 3x}{24x} and \frac{8\left(x-8\right)}{24x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13\times 3x-8\left(x-8\right)}{24x}$$

Do the multiplications in 13\times 3x-8\left(x-8\right).

$$\frac{39x-8x+64}{24x}$$

Combine like terms in 39x-8x+64.

$$\frac{31x+64}{24x}$$

Expand

$$\frac{31}{24}+\frac{8}{3x}$$

Short Solution Steps

Combine x and 12x to get 13x.

$$\frac{13x}{8x}-\frac{x-8}{3x}$$

Cancel out x in both numerator and denominator.

$$\frac{13}{8}-\frac{x-8}{3x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 3x is 24x. Multiply \frac{13}{8} times \frac{3x}{3x}. Multiply \frac{x-8}{3x} times \frac{8}{8}.

$$\frac{13\times 3x}{24x}-\frac{8\left(x-8\right)}{24x}$$

Since \frac{13\times 3x}{24x} and \frac{8\left(x-8\right)}{24x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13\times 3x-8\left(x-8\right)}{24x}$$

Do the multiplications in 13\times 3x-8\left(x-8\right).

$$\frac{39x-8x+64}{24x}$$

Combine like terms in 39x-8x+64.

$$\frac{31x+64}{24x}$$