Solve 2-3/x+1/3-frac{2x{x+1}}

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 2x+2-3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in 3x+3-2x.

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

Divide \frac{2x-1}{x+1} by \frac{x+3}{x+1} by multiplying \frac{2x-1}{x+1} by the reciprocal of \frac{x+3}{x+1}.

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 2x+2-3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+1}{x+1}.

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

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

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

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

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

Combine like terms in 3x+3-2x.

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

Divide \frac{2x-1}{x+1} by \frac{x+3}{x+1} by multiplying \frac{2x-1}{x+1} by the reciprocal of \frac{x+3}{x+1}.

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

Cancel out x+1 in both numerator and denominator.

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