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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-1 and 3x is 3x\left(2x-1\right). Multiply \frac{1}{2x-1} times \frac{3x}{3x}. Multiply \frac{2x+1}{3x} times \frac{2x-1}{2x-1}.

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

Since \frac{3x}{3x\left(2x-1\right)} and \frac{\left(2x+1\right)\left(2x-1\right)}{3x\left(2x-1\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

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

Expand 3x\left(2x-1\right).

$$\frac{3x-4x^{2}+1}{6x^{2}-3x}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-1 and 3x is 3x\left(2x-1\right). Multiply \frac{1}{2x-1} times \frac{3x}{3x}. Multiply \frac{2x+1}{3x} times \frac{2x-1}{2x-1}.

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

Since \frac{3x}{3x\left(2x-1\right)} and \frac{\left(2x+1\right)\left(2x-1\right)}{3x\left(2x-1\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

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

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

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

Expand 3x\left(2x-1\right).

$$\frac{3x-4x^{2}+1}{6x^{2}-3x}$$