Solve 8x-56/8x+48*x^2+9x+18/8x^2+24x

$$\frac{ 8x-56 }{ 8x+48 } \times \frac{ { x }^{ 2 } +9x+18 }{ 8 { x }^{ 2 } +24x }$$

Evaluate

$$\frac{1}{8}-\frac{7}{8x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x-56}{8x+48}.

$$\frac{8\left(x-7\right)}{8\left(x+6\right)}\times \frac{x^{2}+9x+18}{8x^{2}+24x}$$

Cancel out 8 in both numerator and denominator.

$$\frac{x-7}{x+6}\times \frac{x^{2}+9x+18}{8x^{2}+24x}$$

Factor the expressions that are not already factored in \frac{x^{2}+9x+18}{8x^{2}+24x}.

$$\frac{x-7}{x+6}\times \frac{\left(x+3\right)\left(x+6\right)}{8x\left(x+3\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x-7}{x+6}\times \frac{x+6}{8x}$$

Multiply \frac{x-7}{x+6} times \frac{x+6}{8x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-7\right)\left(x+6\right)}{\left(x+6\right)\times 8x}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x-7}{8x}$$

Expand

$$\frac{1}{8}-\frac{7}{8x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{8x-56}{8x+48}.

$$\frac{8\left(x-7\right)}{8\left(x+6\right)}\times \frac{x^{2}+9x+18}{8x^{2}+24x}$$

Cancel out 8 in both numerator and denominator.

$$\frac{x-7}{x+6}\times \frac{x^{2}+9x+18}{8x^{2}+24x}$$

Factor the expressions that are not already factored in \frac{x^{2}+9x+18}{8x^{2}+24x}.

$$\frac{x-7}{x+6}\times \frac{\left(x+3\right)\left(x+6\right)}{8x\left(x+3\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x-7}{x+6}\times \frac{x+6}{8x}$$

Multiply \frac{x-7}{x+6} times \frac{x+6}{8x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-7\right)\left(x+6\right)}{\left(x+6\right)\times 8x}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x-7}{8x}$$