Solve 4c^2-36/8c^2-24c/frac{12c+36{2c^2-6c}}=

$$\frac { \frac { 4 c ^ { 2 } - 36 } { 8 c ^ { 2 } - 24 c } } { \frac { 12 c + 36 } { 2 c ^ { 2 } - 6 c } } =$$

Evaluate

$$\frac{c-3}{12}$$

Short Solution Steps

Divide \frac{4c^{2}-36}{8c^{2}-24c} by \frac{12c+36}{2c^{2}-6c} by multiplying \frac{4c^{2}-36}{8c^{2}-24c} by the reciprocal of \frac{12c+36}{2c^{2}-6c}.

$$\frac{\left(4c^{2}-36\right)\left(2c^{2}-6c\right)}{\left(8c^{2}-24c\right)\left(12c+36\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 4c\left(c+3\right)\left(c-3\right)^{2}}{8\times 12c\left(c-3\right)\left(c+3\right)}$$

Cancel out 2\times 4c\left(c-3\right)\left(c+3\right) in both numerator and denominator.

$$\frac{c-3}{12}$$

Expand

$$\frac{c}{12}-\frac{1}{4}$$

Short Solution Steps

Divide \frac{4c^{2}-36}{8c^{2}-24c} by \frac{12c+36}{2c^{2}-6c} by multiplying \frac{4c^{2}-36}{8c^{2}-24c} by the reciprocal of \frac{12c+36}{2c^{2}-6c}.

$$\frac{\left(4c^{2}-36\right)\left(2c^{2}-6c\right)}{\left(8c^{2}-24c\right)\left(12c+36\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 4c\left(c+3\right)\left(c-3\right)^{2}}{8\times 12c\left(c-3\right)\left(c+3\right)}$$

Cancel out 2\times 4c\left(c-3\right)\left(c+3\right) in both numerator and denominator.

$$\frac{c-3}{12}$$