Solve frac{a^{3}+b^{3}+c^3-3abc}{(a-b)^2+(b-c)^2+(c-a)^2}

$$\frac { a ^ { 3 } + b ^ { 3 } + c ^ { 3 } - 3 a b c } { ( a - b ) ^ { 2 } + ( b - c ) ^ { 2 } + ( c - a ) ^ { 2 } }$$

Evaluate

$$\frac{a+b+c}{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(a+b+c\right)\left(a^{2}-ab-ac+b^{2}-bc+c^{2}\right)}{2\left(a^{2}-ab-ac+b^{2}-bc+c^{2}\right)}$$

Cancel out a^{2}-ab-ac+b^{2}-bc+c^{2} in both numerator and denominator.

$$\frac{a+b+c}{2}$$

Expand

$$\frac{a+b+c}{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(a+b+c\right)\left(a^{2}-ab-ac+b^{2}-bc+c^{2}\right)}{2\left(a^{2}-ab-ac+b^{2}-bc+c^{2}\right)}$$

Cancel out a^{2}-ab-ac+b^{2}-bc+c^{2} in both numerator and denominator.

$$\frac{a+b+c}{2}$$