Solve 3x^2+11x+15+12/x-2

$$3 x ^ { 2 } + 11 x + 15 + \frac { 12 } { x - 2 }$$

Evaluate

$$\frac{3x^{3}+5x^{2}-7x-18}{x-2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{2}+11x+15 times \frac{x-2}{x-2}.

$$\frac{\left(3x^{2}+11x+15\right)\left(x-2\right)}{x-2}+\frac{12}{x-2}$$

Since \frac{\left(3x^{2}+11x+15\right)\left(x-2\right)}{x-2} and \frac{12}{x-2} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x^{2}+11x+15\right)\left(x-2\right)+12}{x-2}$$

Do the multiplications in \left(3x^{2}+11x+15\right)\left(x-2\right)+12.

$$\frac{3x^{3}-6x^{2}+11x^{2}-22x+15x-30+12}{x-2}$$

Combine like terms in 3x^{3}-6x^{2}+11x^{2}-22x+15x-30+12.

$$\frac{3x^{3}+5x^{2}-7x-18}{x-2}$$

Differentiate w.r.t. x

$$\frac{\left(3x-8\right)\left(2x^{2}+x-4\right)}{\left(x-2\right)^{2}}$$