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

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

Evaluate

$$-2x$$

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Divide \frac{-4x^{2}}{1-2x} by \frac{-2x}{2x-1} by multiplying \frac{-4x^{2}}{1-2x} by the reciprocal of \frac{-2x}{2x-1}.

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

Extract the negative sign in 2x-1.

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

Cancel out 2x\left(-2x+1\right) in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

$$-2x$$

Expand

$$-2x$$

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Divide \frac{-4x^{2}}{1-2x} by \frac{-2x}{2x-1} by multiplying \frac{-4x^{2}}{1-2x} by the reciprocal of \frac{-2x}{2x-1}.

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

Extract the negative sign in 2x-1.

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

Cancel out 2x\left(-2x+1\right) in both numerator and denominator.

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

Cancel out -1 in both numerator and denominator.

$$-2x$$