Solve x^2-49/x^2+3x-28*x^2+7x+12/x^2-4x-21

$$\frac { x ^ { 2 } - 49 } { x ^ { 2 } + 3 x - 28 } \cdot \frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } - 4 x - 21 }$$

Evaluate

$$\frac{x+4}{x-4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-49}{x^{2}+3x-28}.

$$\frac{\left(x-7\right)\left(x+7\right)}{\left(x-4\right)\left(x+7\right)}\times \frac{x^{2}+7x+12}{x^{2}-4x-21}$$

Cancel out x+7 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{2}+7x+12}{x^{2}-4x-21}.

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-7}{x-4}\times \frac{x+4}{x-7}$$

Multiply \frac{x-7}{x-4} times \frac{x+4}{x-7} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-7 in both numerator and denominator.

$$\frac{x+4}{x-4}$$

Expand

$$\frac{x+4}{x-4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-49}{x^{2}+3x-28}.

$$\frac{\left(x-7\right)\left(x+7\right)}{\left(x-4\right)\left(x+7\right)}\times \frac{x^{2}+7x+12}{x^{2}-4x-21}$$

Cancel out x+7 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{2}+7x+12}{x^{2}-4x-21}.

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-7}{x-4}\times \frac{x+4}{x-7}$$

Multiply \frac{x-7}{x-4} times \frac{x+4}{x-7} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x-7 in both numerator and denominator.

$$\frac{x+4}{x-4}$$