Solve 4x^2+13-2/x+2

$$4 x ^ { 2 } + 13 - \frac { 2 } { x + 2 }$$

Evaluate

$$\frac{4x^{3}+8x^{2}+13x+24}{x+2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x^{2}+13 times \frac{x+2}{x+2}.

$$\frac{\left(4x^{2}+13\right)\left(x+2\right)}{x+2}-\frac{2}{x+2}$$

Since \frac{\left(4x^{2}+13\right)\left(x+2\right)}{x+2} and \frac{2}{x+2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(4x^{2}+13\right)\left(x+2\right)-2}{x+2}$$

Do the multiplications in \left(4x^{2}+13\right)\left(x+2\right)-2.

$$\frac{4x^{3}+8x^{2}+13x+26-2}{x+2}$$

Combine like terms in 4x^{3}+8x^{2}+13x+26-2.

$$\frac{4x^{3}+8x^{2}+13x+24}{x+2}$$

Differentiate w.r.t. x

$$\frac{2\left(4x^{3}+16x^{2}+16x+1\right)}{\left(x+2\right)^{2}}$$