Solve x^2+14x+49/3x^2+25x+28*3x^2-5x-12/x+7

$$\frac { x ^ { 2 } + 14 x + 49 } { 3 x ^ { 2 } + 25 x + 28 } \cdot \frac { 3 x ^ { 2 } - 5 x - 12 } { x + 7 }$$

Evaluate

$$x-3$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+14x+49}{3x^{2}+25x+28}.

$$\frac{\left(x+7\right)^{2}}{\left(x+7\right)\left(3x+4\right)}\times \frac{3x^{2}-5x-12}{x+7}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{x+7}{3x+4}\times \frac{3x^{2}-5x-12}{x+7}$$

Multiply \frac{x+7}{3x+4} times \frac{3x^{2}-5x-12}{x+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+7\right)\left(3x^{2}-5x-12\right)}{\left(3x+4\right)\left(x+7\right)}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{3x^{2}-5x-12}{3x+4}$$

Factor the expressions that are not already factored.

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

Cancel out 3x+4 in both numerator and denominator.

$$x-3$$

Expand

$$x-3$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+14x+49}{3x^{2}+25x+28}.

$$\frac{\left(x+7\right)^{2}}{\left(x+7\right)\left(3x+4\right)}\times \frac{3x^{2}-5x-12}{x+7}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{x+7}{3x+4}\times \frac{3x^{2}-5x-12}{x+7}$$

Multiply \frac{x+7}{3x+4} times \frac{3x^{2}-5x-12}{x+7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+7\right)\left(3x^{2}-5x-12\right)}{\left(3x+4\right)\left(x+7\right)}$$

Cancel out x+7 in both numerator and denominator.

$$\frac{3x^{2}-5x-12}{3x+4}$$

Factor the expressions that are not already factored.

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

Cancel out 3x+4 in both numerator and denominator.

$$x-3$$