Solve x^2+3x+2/x^2+4x+3*x^2-9/3x+6

$$\frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } + 4 x + 3 } \times \frac { x ^ { 2 } - 9 } { 3 x + 6 }$$

Evaluate

$$\frac{x}{3}-1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+3x+2}{x^{2}+4x+3}.

$$\frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+3\right)}\times \frac{x^{2}-9}{3x+6}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{x+2}{x+3}\times \frac{x^{2}-9}{3x+6}$$

Multiply \frac{x+2}{x+3} times \frac{x^{2}-9}{3x+6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x^{2}-9\right)}{\left(x+3\right)\left(3x+6\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x+2\right)\left(x+3\right) in both numerator and denominator.

$$\frac{x-3}{3}$$

Expand

$$\frac{x}{3}-1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+3x+2}{x^{2}+4x+3}.

$$\frac{\left(x+1\right)\left(x+2\right)}{\left(x+1\right)\left(x+3\right)}\times \frac{x^{2}-9}{3x+6}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{x+2}{x+3}\times \frac{x^{2}-9}{3x+6}$$

Multiply \frac{x+2}{x+3} times \frac{x^{2}-9}{3x+6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x^{2}-9\right)}{\left(x+3\right)\left(3x+6\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x+2\right)\left(x+3\right) in both numerator and denominator.

$$\frac{x-3}{3}$$