Solve c^2-11(+30)/(c-6)(c-5

$$c ^ { 2 } - 11 ( + 30 ) / ( c - 6 ) ( c - 5$$

Evaluate

$$\frac{c^{3}-6c^{2}-330c+1650}{c-6}$$

Short Solution Steps

Multiply 11 and 30 to get 330.

$$c^{2}-\frac{330}{c-6}\left(c-5\right)$$

Express \frac{330}{c-6}\left(c-5\right) as a single fraction.

$$c^{2}-\frac{330\left(c-5\right)}{c-6}$$

Use the distributive property to multiply 330 by c-5.

$$c^{2}-\frac{330c-1650}{c-6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply c^{2} times \frac{c-6}{c-6}.

$$\frac{c^{2}\left(c-6\right)}{c-6}-\frac{330c-1650}{c-6}$$

Since \frac{c^{2}\left(c-6\right)}{c-6} and \frac{330c-1650}{c-6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{c^{2}\left(c-6\right)-\left(330c-1650\right)}{c-6}$$

Do the multiplications in c^{2}\left(c-6\right)-\left(330c-1650\right).

$$\frac{c^{3}-6c^{2}-330c+1650}{c-6}$$

Differentiate w.r.t. c

$$\frac{2\left(c^{3}-12c^{2}+36c+165\right)}{\left(c-6\right)^{2}}$$