Solve x^3-2x^2-13x/2+3/x+2

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

Evaluate

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

Short Solution Steps

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

$$\frac{\frac{2\left(x^{3}-2x^{2}+3\right)}{2}-\frac{13x}{2}}{x+2}$$

Since \frac{2\left(x^{3}-2x^{2}+3\right)}{2} and \frac{13x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2\left(x^{3}-2x^{2}+3\right)-13x}{2}}{x+2}$$

Do the multiplications in 2\left(x^{3}-2x^{2}+3\right)-13x.

$$\frac{\frac{2x^{3}-4x^{2}+6-13x}{2}}{x+2}$$

Express \frac{\frac{2x^{3}-4x^{2}+6-13x}{2}}{x+2} as a single fraction.

$$\frac{2x^{3}-4x^{2}+6-13x}{2\left(x+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{\frac{2\left(x^{3}-2x^{2}+3\right)}{2}-\frac{13x}{2}}{x+2}$$

Since \frac{2\left(x^{3}-2x^{2}+3\right)}{2} and \frac{13x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2\left(x^{3}-2x^{2}+3\right)-13x}{2}}{x+2}$$

Do the multiplications in 2\left(x^{3}-2x^{2}+3\right)-13x.

$$\frac{\frac{2x^{3}-4x^{2}+6-13x}{2}}{x+2}$$

Express \frac{\frac{2x^{3}-4x^{2}+6-13x}{2}}{x+2} as a single fraction.

$$\frac{2x^{3}-4x^{2}+6-13x}{2\left(x+2\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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