Solve x^2-3x-10+11/x+2

$$x ^ { 2 } - 3 x - 10 + \frac { 11 } { x + 2 }$$

Evaluate

$$\frac{x^{3}-x^{2}-16x-9}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}-3x-10 times \frac{x+2}{x+2}.

$$\frac{\left(x^{2}-3x-10\right)\left(x+2\right)}{x+2}+\frac{11}{x+2}$$

Since \frac{\left(x^{2}-3x-10\right)\left(x+2\right)}{x+2} and \frac{11}{x+2} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}-3x-10\right)\left(x+2\right)+11}{x+2}$$

Do the multiplications in \left(x^{2}-3x-10\right)\left(x+2\right)+11.

$$\frac{x^{3}+2x^{2}-3x^{2}-6x-10x-20+11}{x+2}$$

Combine like terms in x^{3}+2x^{2}-3x^{2}-6x-10x-20+11.

$$\frac{x^{3}-x^{2}-16x-9}{x+2}$$

Differentiate w.r.t. x

$$\frac{2x^{3}+5x^{2}-4x-23}{\left(x+2\right)^{2}}$$