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

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

Evaluate

$$\frac{1}{x-2}$$

Short Solution Steps

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

$$\frac{x+3}{x^{2}-4x+4}\times \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x+3\right)}$$

Cancel out x+1 in both numerator and denominator.

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

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

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-2}{x^{2}-4x+4}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{1}{x-2}$$

Expand

$$\frac{1}{x-2}$$

Short Solution Steps

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

$$\frac{x+3}{x^{2}-4x+4}\times \frac{\left(x-2\right)\left(x+1\right)}{\left(x+1\right)\left(x+3\right)}$$

Cancel out x+1 in both numerator and denominator.

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

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

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-2}{x^{2}-4x+4}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{1}{x-2}$$