Solve 2x+16/x^2+3x-40*x^2-11x+30/x^2-14x+48

$$\frac { 2 x + 16 } { x ^ { 2 } + 3 x - 40 } \cdot \frac { x ^ { 2 } - 11 x + 30 } { x ^ { 2 } - 14 x + 48 }$$

Evaluate

$$\frac{2}{x-8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x+16}{x^{2}+3x-40}.

$$\frac{2\left(x+8\right)}{\left(x-5\right)\left(x+8\right)}\times \frac{x^{2}-11x+30}{x^{2}-14x+48}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{2}{x-5}\times \frac{x^{2}-11x+30}{x^{2}-14x+48}$$

Factor the expressions that are not already factored in \frac{x^{2}-11x+30}{x^{2}-14x+48}.

$$\frac{2}{x-5}\times \frac{\left(x-6\right)\left(x-5\right)}{\left(x-8\right)\left(x-6\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{2}{x-5}\times \frac{x-5}{x-8}$$

Multiply \frac{2}{x-5} times \frac{x-5}{x-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-8\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{2}{x-8}$$

Expand

$$\frac{2}{x-8}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x+16}{x^{2}+3x-40}.

$$\frac{2\left(x+8\right)}{\left(x-5\right)\left(x+8\right)}\times \frac{x^{2}-11x+30}{x^{2}-14x+48}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{2}{x-5}\times \frac{x^{2}-11x+30}{x^{2}-14x+48}$$

Factor the expressions that are not already factored in \frac{x^{2}-11x+30}{x^{2}-14x+48}.

$$\frac{2}{x-5}\times \frac{\left(x-6\right)\left(x-5\right)}{\left(x-8\right)\left(x-6\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{2}{x-5}\times \frac{x-5}{x-8}$$

Multiply \frac{2}{x-5} times \frac{x-5}{x-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-8\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{2}{x-8}$$