Solve 3x+5/x+1+x^2+x/x+1+x+1/x+1

$$\frac{ 3x+5 }{ x+1 } + \frac{ { x }^{ 2 } +x }{ x+1 } + \frac{ x+1 }{ x+1 }$$

Evaluate

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

Short Solution Steps

Divide x+1 by x+1 to get 1.

$$\frac{3x+5}{x+1}+\frac{x^{2}+x}{x+1}+1$$

Factor the expressions that are not already factored in \frac{x^{2}+x}{x+1}.

$$\frac{3x+5}{x+1}+\frac{x\left(x+1\right)}{x+1}+1$$

Cancel out x+1 in both numerator and denominator.

$$\frac{3x+5}{x+1}+x+1$$

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

$$\frac{3x+5}{x+1}+\frac{\left(x+1\right)\left(x+1\right)}{x+1}$$

Since \frac{3x+5}{x+1} and \frac{\left(x+1\right)\left(x+1\right)}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{3x+5+\left(x+1\right)\left(x+1\right)}{x+1}$$

Do the multiplications in 3x+5+\left(x+1\right)\left(x+1\right).

$$\frac{3x+5+x^{2}+x+x+1}{x+1}$$

Combine like terms in 3x+5+x^{2}+x+x+1.

$$\frac{5x+6+x^{2}}{x+1}$$

Expand

$$\frac{x^{2}+5x+6}{x+1}$$

Short Solution Steps

Divide x+1 by x+1 to get 1.

$$\frac{3x+5}{x+1}+\frac{x^{2}+x}{x+1}+1$$

Factor the expressions that are not already factored in \frac{x^{2}+x}{x+1}.

$$\frac{3x+5}{x+1}+\frac{x\left(x+1\right)}{x+1}+1$$

Cancel out x+1 in both numerator and denominator.

$$\frac{3x+5}{x+1}+x+1$$

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

$$\frac{3x+5}{x+1}+\frac{\left(x+1\right)\left(x+1\right)}{x+1}$$

Since \frac{3x+5}{x+1} and \frac{\left(x+1\right)\left(x+1\right)}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{3x+5+\left(x+1\right)\left(x+1\right)}{x+1}$$

Do the multiplications in 3x+5+\left(x+1\right)\left(x+1\right).

$$\frac{3x+5+x^{2}+x+x+1}{x+1}$$

Combine like terms in 3x+5+x^{2}+x+x+1.

$$\frac{5x+6+x^{2}}{x+1}$$