Solve x^2-49/x+2*x^2+8x+12/x^2-x-42

$$\frac { x ^ { 2 } - 49 } { x + 2 } \cdot \frac { x ^ { 2 } + 8 x + 12 } { x ^ { 2 } - x - 42 }$$

Evaluate

$$x+7$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+8x+12}{x^{2}-x-42}.

$$\frac{x^{2}-49}{x+2}\times \frac{\left(x+2\right)\left(x+6\right)}{\left(x-7\right)\left(x+6\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x^{2}-49}{x+2}\times \frac{x+2}{x-7}$$

Multiply \frac{x^{2}-49}{x+2} times \frac{x+2}{x-7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-49\right)\left(x+2\right)}{\left(x+2\right)\left(x-7\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x^{2}-49}{x-7}$$

Factor the expressions that are not already factored.

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

Cancel out x-7 in both numerator and denominator.

$$x+7$$

Expand

$$x+7$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+8x+12}{x^{2}-x-42}.

$$\frac{x^{2}-49}{x+2}\times \frac{\left(x+2\right)\left(x+6\right)}{\left(x-7\right)\left(x+6\right)}$$

Cancel out x+6 in both numerator and denominator.

$$\frac{x^{2}-49}{x+2}\times \frac{x+2}{x-7}$$

Multiply \frac{x^{2}-49}{x+2} times \frac{x+2}{x-7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-49\right)\left(x+2\right)}{\left(x+2\right)\left(x-7\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x^{2}-49}{x-7}$$

Factor the expressions that are not already factored.

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

Cancel out x-7 in both numerator and denominator.

$$x+7$$