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

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

Evaluate

$$\frac{x^{4}+6x^{3}+8x^{2}+15x+5}{x+5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}+x^{2}+3x times \frac{x+5}{x+5}.

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

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

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

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

$$\frac{x^{4}+5x^{3}+x^{3}+5x^{2}+3x^{2}+15x+5}{x+5}$$

Combine like terms in x^{4}+5x^{3}+x^{3}+5x^{2}+3x^{2}+15x+5.

$$\frac{x^{4}+6x^{3}+8x^{2}+15x+5}{x+5}$$

Differentiate w.r.t. x

$$\frac{3x^{4}+32x^{3}+98x^{2}+80x+70}{\left(x+5\right)^{2}}$$