Solve frac{2(x+z+y)+sqrt{2(left(x-yright)^2+left(x-zright)^2+left(y-zright)^2}}{6}

$$\frac{ 2(x+z+y)+ \sqrt{ 2( { \left(x-y \right) }^{ 2 } + { \left(x-z \right) }^{ 2 } + { \left(y-z \right) }^{ 2 } } }{ 6 }$$

Factor

$$\frac{\sqrt{x^{2}-xy-xz+y^{2}-yz+z^{2}}+6x+6y+6z}{3}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{12\left(x+z+y\right)+\sqrt{2}\sqrt{\left(x-y\right)^{2}+\left(x-z\right)^{2}+\left(y-z\right)^{2}}}{6}$$

Evaluate

$$\frac{\sqrt{x^{2}-xy-xz+y^{2}-yz+z^{2}}}{3}+2x+2y+2z$$