Solve 2x+2y/6(x-y)*3x-3y/x^2+2xy+y^2=

$$\frac { 2 x + 2 y } { 6 ( x - y ) } \cdot \frac { 3 x - 3 y } { x ^ { 2 } + 2 x y + y ^ { 2 } } =$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x+2y}{6\left(x-y\right)}.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{x+y}{3\left(x-y\right)} times \frac{3x-3y}{x^{2}+2xy+y^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

Cancel out 3\left(x+y\right)\left(x-y\right) 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{2x+2y}{6\left(x-y\right)}.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{x+y}{3\left(x-y\right)} times \frac{3x-3y}{x^{2}+2xy+y^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

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