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

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

Evaluate

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

Short Solution Steps

Combine x and 3x to get 4x.

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

Combine x and -3x to get -2x.

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

Cancel out 2 and 2.

$$\frac{4x-3x^{2}-1}{2x-1}-\left(-x\right)$$

The opposite of -x is x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2x-1}{2x-1}.

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

Since \frac{4x-3x^{2}-1}{2x-1} and \frac{x\left(2x-1\right)}{2x-1} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4x-3x^{2}-1+x\left(2x-1\right).

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

Combine like terms in 4x-3x^{2}-1+2x^{2}-x.

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

Expand

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

Short Solution Steps

Combine x and 3x to get 4x.

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

Combine x and -3x to get -2x.

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

Cancel out 2 and 2.

$$\frac{4x-3x^{2}-1}{2x-1}-\left(-x\right)$$

The opposite of -x is x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2x-1}{2x-1}.

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

Since \frac{4x-3x^{2}-1}{2x-1} and \frac{x\left(2x-1\right)}{2x-1} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4x-3x^{2}-1+x\left(2x-1\right).

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

Combine like terms in 4x-3x^{2}-1+2x^{2}-x.

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