Solve x^2-2x/3x+2div(1+2/x-4)

$$\frac { x ^ { 2 } - 2 x } { 3 x + 2 } \div ( 1 + \frac { 2 } { x - 4 } )$$

Evaluate

$$\frac{x\left(x-4\right)}{3x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-4}{x-4}.

$$\frac{\frac{x^{2}-2x}{3x+2}}{\frac{x-4}{x-4}+\frac{2}{x-4}}$$

Since \frac{x-4}{x-4} and \frac{2}{x-4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-2x}{3x+2}}{\frac{x-4+2}{x-4}}$$

Combine like terms in x-4+2.

$$\frac{\frac{x^{2}-2x}{3x+2}}{\frac{x-2}{x-4}}$$

Divide \frac{x^{2}-2x}{3x+2} by \frac{x-2}{x-4} by multiplying \frac{x^{2}-2x}{3x+2} by the reciprocal of \frac{x-2}{x-4}.

$$\frac{\left(x^{2}-2x\right)\left(x-4\right)}{\left(3x+2\right)\left(x-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-4\right)\left(x-2\right)}{\left(x-2\right)\left(3x+2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x\left(x-4\right)}{3x+2}$$

Expand the expression.

$$\frac{x^{2}-4x}{3x+2}$$

Expand

$$\frac{x^{2}-4x}{3x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-4}{x-4}.

$$\frac{\frac{x^{2}-2x}{3x+2}}{\frac{x-4}{x-4}+\frac{2}{x-4}}$$

Since \frac{x-4}{x-4} and \frac{2}{x-4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x^{2}-2x}{3x+2}}{\frac{x-4+2}{x-4}}$$

Combine like terms in x-4+2.

$$\frac{\frac{x^{2}-2x}{3x+2}}{\frac{x-2}{x-4}}$$

Divide \frac{x^{2}-2x}{3x+2} by \frac{x-2}{x-4} by multiplying \frac{x^{2}-2x}{3x+2} by the reciprocal of \frac{x-2}{x-4}.

$$\frac{\left(x^{2}-2x\right)\left(x-4\right)}{\left(3x+2\right)\left(x-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-4\right)\left(x-2\right)}{\left(x-2\right)\left(3x+2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x\left(x-4\right)}{3x+2}$$

Expand the expression.

$$\frac{x^{2}-4x}{3x+2}$$