Solve x^2+3x+5div(x+1)

$${ x }^{ 2 } +3x+5 \div (x+1)$$

Evaluate

$$\frac{x^{3}+4x^{2}+3x+5}{x+1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+3x times \frac{x+1}{x+1}.

$$\frac{\left(x^{2}+3x\right)\left(x+1\right)}{x+1}+\frac{5}{x+1}$$

Since \frac{\left(x^{2}+3x\right)\left(x+1\right)}{x+1} and \frac{5}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+3x\right)\left(x+1\right)+5}{x+1}$$

Do the multiplications in \left(x^{2}+3x\right)\left(x+1\right)+5.

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

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

$$\frac{x^{3}+4x^{2}+3x+5}{x+1}$$

Differentiate w.r.t. x

$$\frac{2x^{3}+7x^{2}+8x-2}{\left(x+1\right)^{2}}$$