Solve ((2x+1)div(x+1))div(1-2xdiv(x+1)

$$((2x+1) \div (x+1)) \div (1-2x \div (x+1)$$

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in x+1-2x.

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

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

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in x+1-2x.

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

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

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

Cancel out x+1 in both numerator and denominator.

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