Solve frac{x^{2}+y^{2}-z^2+2xy}{x^2+y^2+z^2+2xy+2xz+2yz}

$$\frac { x ^ { 2 } + y ^ { 2 } - z ^ { 2 } + 2 x y } { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 2 x y + 2 x z + 2 y z }$$

Evaluate

$$\frac{x+y-z}{x+y+z}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out x+y+z in both numerator and denominator.

$$\frac{x+y-z}{x+y+z}$$

Expand

$$\frac{x+y-z}{x+y+z}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out x+y+z in both numerator and denominator.

$$\frac{x+y-z}{x+y+z}$$