Solve x^2+14x+48/x^2+3x-28*x^2-3x-4/x^2+6x-16

$$\frac { x ^ { 2 } + 14 x + 48 } { x ^ { 2 } + 3 x - 28 } \cdot \frac { x ^ { 2 } - 3 x - 4 } { x ^ { 2 } + 6 x - 16 }$$

Evaluate

$$\frac{\left(x+1\right)\left(x+6\right)}{\left(x-2\right)\left(x+7\right)}$$

Short Solution Steps

Multiply \frac{x^{2}+14x+48}{x^{2}+3x-28} times \frac{x^{2}-3x-4}{x^{2}+6x-16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+14x+48\right)\left(x^{2}-3x-4\right)}{\left(x^{2}+3x-28\right)\left(x^{2}+6x-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-4\right)\left(x+1\right)\left(x+6\right)\left(x+8\right)}{\left(x-4\right)\left(x-2\right)\left(x+7\right)\left(x+8\right)}$$

Cancel out \left(x-4\right)\left(x+8\right) in both numerator and denominator.

$$\frac{\left(x+1\right)\left(x+6\right)}{\left(x-2\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{x^{2}+7x+6}{x^{2}+5x-14}$$

Expand

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

Short Solution Steps

Multiply \frac{x^{2}+14x+48}{x^{2}+3x-28} times \frac{x^{2}-3x-4}{x^{2}+6x-16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+14x+48\right)\left(x^{2}-3x-4\right)}{\left(x^{2}+3x-28\right)\left(x^{2}+6x-16\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-4\right)\left(x+1\right)\left(x+6\right)\left(x+8\right)}{\left(x-4\right)\left(x-2\right)\left(x+7\right)\left(x+8\right)}$$

Cancel out \left(x-4\right)\left(x+8\right) in both numerator and denominator.

$$\frac{\left(x+1\right)\left(x+6\right)}{\left(x-2\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{x^{2}+7x+6}{x^{2}+5x-14}$$