Solve x^3-2x^2-5x+6:(x-1)

$$x ^ { 3 } - 2 x ^ { 2 } - 5 x + 6 : ( x - 1 )$$

Evaluate

$$\frac{x^{4}-3x^{3}-3x^{2}+5x+6}{x-1}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}-2x^{2}-5x times \frac{x-1}{x-1}.

$$\frac{\left(x^{3}-2x^{2}-5x\right)\left(x-1\right)}{x-1}+\frac{6}{x-1}$$

Since \frac{\left(x^{3}-2x^{2}-5x\right)\left(x-1\right)}{x-1} and \frac{6}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{3}-2x^{2}-5x\right)\left(x-1\right)+6}{x-1}$$

Do the multiplications in \left(x^{3}-2x^{2}-5x\right)\left(x-1\right)+6.

$$\frac{x^{4}-x^{3}-2x^{3}+2x^{2}-5x^{2}+5x+6}{x-1}$$

Combine like terms in x^{4}-x^{3}-2x^{3}+2x^{2}-5x^{2}+5x+6.

$$\frac{x^{4}-3x^{3}-3x^{2}+5x+6}{x-1}$$

Differentiate w.r.t. x

$$\frac{3x^{4}-10x^{3}+6x^{2}+6x-11}{\left(x-1\right)^{2}}$$