Solve x^2-16/x^2+7x+12*x^2-4x-21/x^2-4x

$$\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 7 x + 12 } \cdot \frac { x ^ { 2 } - 4 x - 21 } { x ^ { 2 } - 4 x }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-16}{x^{2}+7x+12}.

$$\frac{\left(x-4\right)\left(x+4\right)}{\left(x+3\right)\left(x+4\right)}\times \frac{x^{2}-4x-21}{x^{2}-4x}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x-4}{x+3}\times \frac{x^{2}-4x-21}{x^{2}-4x}$$

Multiply \frac{x-4}{x+3} times \frac{x^{2}-4x-21}{x^{2}-4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x^{2}-4x-21\right)}{\left(x+3\right)\left(x^{2}-4x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x-4\right)\left(x+3\right)}{x\left(x-4\right)\left(x+3\right)}$$

Cancel out \left(x-4\right)\left(x+3\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-16}{x^{2}+7x+12}.

$$\frac{\left(x-4\right)\left(x+4\right)}{\left(x+3\right)\left(x+4\right)}\times \frac{x^{2}-4x-21}{x^{2}-4x}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x-4}{x+3}\times \frac{x^{2}-4x-21}{x^{2}-4x}$$

Multiply \frac{x-4}{x+3} times \frac{x^{2}-4x-21}{x^{2}-4x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x^{2}-4x-21\right)}{\left(x+3\right)\left(x^{2}-4x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x-4\right)\left(x+3\right)}{x\left(x-4\right)\left(x+3\right)}$$

Cancel out \left(x-4\right)\left(x+3\right) in both numerator and denominator.

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