Solve x^2+7+5/x-1*S

$$x ^ { 2 } + 7 + \frac { 5 } { x - 1 } \cdot S$$

Evaluate

$$\frac{x^{3}-x^{2}+7x+5S-7}{x-1}$$

Short Solution Steps

Express \frac{5}{x-1}S as a single fraction.

$$x^{2}+7+\frac{5S}{x-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}+7 times \frac{x-1}{x-1}.

$$\frac{\left(x^{2}+7\right)\left(x-1\right)}{x-1}+\frac{5S}{x-1}$$

Since \frac{\left(x^{2}+7\right)\left(x-1\right)}{x-1} and \frac{5S}{x-1} have the same denominator, add them by adding their numerators.

$$\frac{\left(x^{2}+7\right)\left(x-1\right)+5S}{x-1}$$

Do the multiplications in \left(x^{2}+7\right)\left(x-1\right)+5S.

$$\frac{x^{3}-x^{2}+7x-7+5S}{x-1}$$

Differentiate w.r.t. x

$$\frac{2x^{3}-4x^{2}+2x-5S}{\left(x-1\right)^{2}}$$