Solve 2x^2-72/6x^2+12x-288*x^2+5x-24/x^2+3x-18

$$\frac { 2 x ^ { 2 } - 72 } { 6 x ^ { 2 } + 12 x - 288 } \cdot \frac { x ^ { 2 } + 5 x - 24 } { x ^ { 2 } + 3 x - 18 }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-72}{6x^{2}+12x-288}.

$$\frac{2\left(x-6\right)\left(x+6\right)}{6\left(x-6\right)\left(x+8\right)}\times \frac{x^{2}+5x-24}{x^{2}+3x-18}$$

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

$$\frac{x+6}{3\left(x+8\right)}\times \frac{x^{2}+5x-24}{x^{2}+3x-18}$$

Factor the expressions that are not already factored in \frac{x^{2}+5x-24}{x^{2}+3x-18}.

$$\frac{x+6}{3\left(x+8\right)}\times \frac{\left(x-3\right)\left(x+8\right)}{\left(x-3\right)\left(x+6\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x+6}{3\left(x+8\right)}\times \frac{x+8}{x+6}$$

Multiply \frac{x+6}{3\left(x+8\right)} times \frac{x+8}{x+6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+6\right)\left(x+8\right)}{3\left(x+8\right)\left(x+6\right)}$$

Cancel out \left(x+6\right)\left(x+8\right) in both numerator and denominator.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$