Solve 30c^3-60c^2/3cdiv(2c^3-16c^2+24c)

$$\frac { 30 c ^ { 3 } - 60 c ^ { 2 } } { 3 c } \div ( 2 c ^ { 3 } - 16 c ^ { 2 } + 24 c )$$

Evaluate

$$\frac{5}{c-6}$$

Short Solution Steps

Express \frac{\frac{30c^{3}-60c^{2}}{3c}}{2c^{3}-16c^{2}+24c} as a single fraction.

$$\frac{30c^{3}-60c^{2}}{3c\left(2c^{3}-16c^{2}+24c\right)}$$

Factor the expressions that are not already factored.

$$\frac{30\left(c-2\right)c^{2}}{2\times 3\left(c-6\right)\left(c-2\right)c^{2}}$$

Cancel out 2\times 3\left(c-2\right)c^{2} in both numerator and denominator.

$$\frac{5}{c-6}$$

Expand

$$\frac{5}{c-6}$$

Short Solution Steps

Express \frac{\frac{30c^{3}-60c^{2}}{3c}}{2c^{3}-16c^{2}+24c} as a single fraction.

$$\frac{30c^{3}-60c^{2}}{3c\left(2c^{3}-16c^{2}+24c\right)}$$

Factor the expressions that are not already factored.

$$\frac{30\left(c-2\right)c^{2}}{2\times 3\left(c-6\right)\left(c-2\right)c^{2}}$$

Cancel out 2\times 3\left(c-2\right)c^{2} in both numerator and denominator.

$$\frac{5}{c-6}$$