Solve (2+2/x+1)*(3-6/x+2)*(1+1/x)=

$$( 2 + \frac { 2 } { x + 1 } ) \cdot ( 3 - \frac { 6 } { x + 2 } ) \cdot ( 1 + \frac { 1 } { x } ) =$$

Evaluate

$$6$$

Short Solution Steps

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

$$\left(\frac{2\left(x+1\right)}{x+1}+\frac{2}{x+1}\right)\left(3-\frac{6}{x+2}\right)\left(1+\frac{1}{x}\right)$$

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

$$\frac{2\left(x+1\right)+2}{x+1}\left(3-\frac{6}{x+2}\right)\left(1+\frac{1}{x}\right)$$

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

$$\frac{2x+2+2}{x+1}\left(3-\frac{6}{x+2}\right)\left(1+\frac{1}{x}\right)$$

Combine like terms in 2x+2+2.

$$\frac{2x+4}{x+1}\left(3-\frac{6}{x+2}\right)\left(1+\frac{1}{x}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+2}{x+2}.

$$\frac{2x+4}{x+1}\left(\frac{3\left(x+2\right)}{x+2}-\frac{6}{x+2}\right)\left(1+\frac{1}{x}\right)$$

Since \frac{3\left(x+2\right)}{x+2} and \frac{6}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x+4}{x+1}\times \frac{3\left(x+2\right)-6}{x+2}\left(1+\frac{1}{x}\right)$$

Do the multiplications in 3\left(x+2\right)-6.

$$\frac{2x+4}{x+1}\times \frac{3x+6-6}{x+2}\left(1+\frac{1}{x}\right)$$

Combine like terms in 3x+6-6.

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

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

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

Since \frac{x}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{2x+4}{x+1}\times \frac{3x}{x+2}\times \frac{x+1}{x}$$

Multiply \frac{2x+4}{x+1} times \frac{3x}{x+2} by multiplying numerator times numerator and denominator times denominator.

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

Multiply \frac{\left(2x+4\right)\times 3x}{\left(x+1\right)\left(x+2\right)} times \frac{x+1}{x} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$2\times 3$$

Multiply 2 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$