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

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

Evaluate

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

Short Solution Steps

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

$$\frac{1}{x}+\frac{3x}{x}-4\times \frac{1}{x}-x+3x-2$$

Since \frac{1}{x} and \frac{3x}{x} have the same denominator, add them by adding their numerators.

$$\frac{1+3x}{x}-4\times \frac{1}{x}-x+3x-2$$

Express 4\times \frac{1}{x} as a single fraction.

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

Since \frac{1+3x}{x} and \frac{4}{x} have the same denominator, subtract them by subtracting their numerators.

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

Combine like terms in 1+3x-4.

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

Combine -x and 3x to get 2x.

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

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

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

Since \frac{-3+3x}{x} and \frac{\left(2x-2\right)x}{x} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -3+3x+\left(2x-2\right)x.

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

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

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

Factor

$$\frac{\left(x-1\right)\left(2x+3\right)}{x}$$