Solve 3x^2-2xy+6x-4y/3x^2+xy-2y^2*x-2/x^2-4

$$\frac { 3 x ^ { 2 } - 2 x y + 6 x - 4 y } { 3 x ^ { 2 } + x y - 2 y ^ { 2 } } \cdot \frac { x - 2 } { x ^ { 2 } - 4 }$$

Evaluate

$$\frac{1}{x+y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-2xy+6x-4y}{3x^{2}+xy-2y^{2}}.

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

Cancel out 3x-2y in both numerator and denominator.

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

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

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

Cancel out x-2 in both numerator and denominator.

$$\frac{x+2}{x+y}\times \frac{1}{x+2}$$

Multiply \frac{x+2}{x+y} times \frac{1}{x+2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{1}{x+y}$$

Expand

$$\frac{1}{x+y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}-2xy+6x-4y}{3x^{2}+xy-2y^{2}}.

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

Cancel out 3x-2y in both numerator and denominator.

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

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

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

Cancel out x-2 in both numerator and denominator.

$$\frac{x+2}{x+y}\times \frac{1}{x+2}$$

Multiply \frac{x+2}{x+y} times \frac{1}{x+2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{1}{x+y}$$