Solve 6c^2+13c-63/6c^2-17c+7*2c^2-9c+4/12c+54

$$\frac { 6 c ^ { 2 } + 13 c - 63 } { 6 c ^ { 2 } - 17 c + 7 } \cdot \frac { 2 c ^ { 2 } - 9 c + 4 } { 12 c + 54 }$$

Evaluate

$$\frac{c-4}{6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6c^{2}+13c-63}{6c^{2}-17c+7}.

$$\frac{\left(3c-7\right)\left(2c+9\right)}{\left(2c-1\right)\left(3c-7\right)}\times \frac{2c^{2}-9c+4}{12c+54}$$

Cancel out 3c-7 in both numerator and denominator.

$$\frac{2c+9}{2c-1}\times \frac{2c^{2}-9c+4}{12c+54}$$

Multiply \frac{2c+9}{2c-1} times \frac{2c^{2}-9c+4}{12c+54} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2c+9\right)\left(2c^{2}-9c+4\right)}{\left(2c-1\right)\left(12c+54\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(c-4\right)\left(2c-1\right)\left(2c+9\right)}{6\left(2c-1\right)\left(2c+9\right)}$$

Cancel out \left(2c-1\right)\left(2c+9\right) in both numerator and denominator.

$$\frac{c-4}{6}$$

Expand

$$\frac{c}{6}-\frac{2}{3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{6c^{2}+13c-63}{6c^{2}-17c+7}.

$$\frac{\left(3c-7\right)\left(2c+9\right)}{\left(2c-1\right)\left(3c-7\right)}\times \frac{2c^{2}-9c+4}{12c+54}$$

Cancel out 3c-7 in both numerator and denominator.

$$\frac{2c+9}{2c-1}\times \frac{2c^{2}-9c+4}{12c+54}$$

Multiply \frac{2c+9}{2c-1} times \frac{2c^{2}-9c+4}{12c+54} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2c+9\right)\left(2c^{2}-9c+4\right)}{\left(2c-1\right)\left(12c+54\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(c-4\right)\left(2c-1\right)\left(2c+9\right)}{6\left(2c-1\right)\left(2c+9\right)}$$

Cancel out \left(2c-1\right)\left(2c+9\right) in both numerator and denominator.

$$\frac{c-4}{6}$$