Solve 15x^2-3x-54/5x^2+39x+54*4x^2+12x-72/x^2-5x+6

$$\frac { 15 x ^ { 2 } - 3 x - 54 } { 5 x ^ { 2 } + 39 x + 54 } \cdot \frac { 4 x ^ { 2 } + 12 x - 72 } { x ^ { 2 } - 5 x + 6 }$$

Evaluate

$$12$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{15x^{2}-3x-54}{5x^{2}+39x+54}.

$$\frac{3\left(x-2\right)\left(5x+9\right)}{\left(x+6\right)\left(5x+9\right)}\times \frac{4x^{2}+12x-72}{x^{2}-5x+6}$$

Cancel out 5x+9 in both numerator and denominator.

$$\frac{3\left(x-2\right)}{x+6}\times \frac{4x^{2}+12x-72}{x^{2}-5x+6}$$

Factor the expressions that are not already factored in \frac{4x^{2}+12x-72}{x^{2}-5x+6}.

$$\frac{3\left(x-2\right)}{x+6}\times \frac{4\left(x-3\right)\left(x+6\right)}{\left(x-3\right)\left(x-2\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{3\left(x-2\right)}{x+6}\times \frac{4\left(x+6\right)}{x-2}$$

Multiply \frac{3\left(x-2\right)}{x+6} times \frac{4\left(x+6\right)}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(x-2\right)\times 4\left(x+6\right)}{\left(x+6\right)\left(x-2\right)}$$

Cancel out \left(x-2\right)\left(x+6\right) in both numerator and denominator.

$$3\times 4$$

Multiply 3 and 4 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$