Solve 1-8/x/x+frac{2{3x}}

$$\frac { 1 - \frac { 8 } { x } } { x + \frac { 2 } { 3 x } }$$

Evaluate

$$\frac{3\left(x-8\right)}{3x^{2}+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x}{x}-\frac{8}{x}}{x+\frac{2}{3x}}$$

Since \frac{x}{x} and \frac{8}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-8}{x}}{x+\frac{2}{3x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{3x}{3x}.

$$\frac{\frac{x-8}{x}}{\frac{x\times 3x}{3x}+\frac{2}{3x}}$$

Since \frac{x\times 3x}{3x} and \frac{2}{3x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-8}{x}}{\frac{x\times 3x+2}{3x}}$$

Do the multiplications in x\times 3x+2.

$$\frac{\frac{x-8}{x}}{\frac{3x^{2}+2}{3x}}$$

Divide \frac{x-8}{x} by \frac{3x^{2}+2}{3x} by multiplying \frac{x-8}{x} by the reciprocal of \frac{3x^{2}+2}{3x}.

$$\frac{\left(x-8\right)\times 3x}{x\left(3x^{2}+2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{3\left(x-8\right)}{3x^{2}+2}$$

Use the distributive property to multiply 3 by x-8.

$$\frac{3x-24}{3x^{2}+2}$$

Expand

$$\frac{3\left(x-8\right)}{3x^{2}+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$\frac{\frac{x}{x}-\frac{8}{x}}{x+\frac{2}{3x}}$$

Since \frac{x}{x} and \frac{8}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-8}{x}}{x+\frac{2}{3x}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{3x}{3x}.

$$\frac{\frac{x-8}{x}}{\frac{x\times 3x}{3x}+\frac{2}{3x}}$$

Since \frac{x\times 3x}{3x} and \frac{2}{3x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-8}{x}}{\frac{x\times 3x+2}{3x}}$$

Do the multiplications in x\times 3x+2.

$$\frac{\frac{x-8}{x}}{\frac{3x^{2}+2}{3x}}$$

Divide \frac{x-8}{x} by \frac{3x^{2}+2}{3x} by multiplying \frac{x-8}{x} by the reciprocal of \frac{3x^{2}+2}{3x}.

$$\frac{\left(x-8\right)\times 3x}{x\left(3x^{2}+2\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{3\left(x-8\right)}{3x^{2}+2}$$

Use the distributive property to multiply 3 by x-8.

$$\frac{3x-24}{3x^{2}+2}$$