Solve 1/3x^2-2x4x^2-x

$$\frac { 1 } { 3 x ^ { 2 } - 2 x } 4 x ^ { 2 } - x$$

Evaluate

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

Short Solution Steps

Express \frac{1}{3x^{2}-2x}\times 4 as a single fraction.

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

Express \frac{4}{3x^{2}-2x}x^{2} as a single fraction.

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

Factor 3x^{2}-2x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x\left(3x-2\right)}{x\left(3x-2\right)}.

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

Since \frac{4x^{2}}{x\left(3x-2\right)} and \frac{xx\left(3x-2\right)}{x\left(3x-2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4x^{2}-xx\left(3x-2\right).

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

Combine like terms in 4x^{2}-3x^{3}+2x^{2}.

$$\frac{6x^{2}-3x^{3}}{x\left(3x-2\right)}$$

Factor the expressions that are not already factored in \frac{6x^{2}-3x^{3}}{x\left(3x-2\right)}.

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

Cancel out x in both numerator and denominator.

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

Use the distributive property to multiply 3x by -x+2.

$$\frac{-3x^{2}+6x}{3x-2}$$

Factor

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