What is expand (ab(a+b)+bc(b+c)+ac(a+c))/(3abc) ?

The solution to expand (ab(a+b)+bc(b+c)+ac(a+c))/(3abc) is a/(3c)+b/(3c)+b/(3a)+c/(3a)+a/(3b)+c/(3b)

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expand (ab(a+b)+bc(b+c)+ac(a+c))/(3abc)

expand

\frac{ab ( a + b ) + b c ( b + c ) + a c ( a + c )}{3 ab c}

\frac{a}{3 c} + \frac{b}{3 c} + \frac{b}{3 a} + \frac{c}{3 a} + \frac{a}{3 b} + \frac{c}{3 b}

Solution steps

\frac{ab ( a + b ) + b c ( b + c ) + a c ( a + c )}{3 ab c}

Expand

ab (a + b) + b c (b + c) + a c (a + c) : a^{2} b + a b^{2} + b^{2} c + b c^{2} + a^{2} c + a c^{2}

= \frac{a ^{2} b + a b ^{2} + b ^{2} c + b c ^{2} + a ^{2} c + a c ^{2}}{3 ab c}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{a ^{2} b + a b ^{2} + b ^{2} c + b c ^{2} + a ^{2} c + a c ^{2}}{3 ab c} = \frac{a ^{2} b}{3 ab c} + \frac{a b ^{2}}{3 ab c} + \frac{b ^{2} c}{3 ab c} + \frac{b c ^{2}}{3 ab c} + \frac{a ^{2} c}{3 ab c} + \frac{a c ^{2}}{3 ab c}

= \frac{a ^{2} b}{3 ab c} + \frac{a b ^{2}}{3 ab c} + \frac{b ^{2} c}{3 ab c} + \frac{b c ^{2}}{3 ab c} + \frac{a ^{2} c}{3 ab c} + \frac{a c ^{2}}{3 ab c}

\frac{a ^{2} b}{3 ab c} = \frac{a}{3 c}

\frac{a b ^{2}}{3 ab c} = \frac{b}{3 c}

\frac{b ^{2} c}{3 ab c} = \frac{b}{3 a}

\frac{b c ^{2}}{3 ab c} = \frac{c}{3 a}

\frac{a ^{2} c}{3 ab c} = \frac{a}{3 b}

\frac{a c ^{2}}{3 ab c} = \frac{c}{3 b}

= \frac{a}{3 c} + \frac{b}{3 c} + \frac{b}{3 a} + \frac{c}{3 a} + \frac{a}{3 b} + \frac{c}{3 b}

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What is expand (ab(a+b)+bc(b+c)+ac(a+c))/(3abc) ?
The solution to expand (ab(a+b)+bc(b+c)+ac(a+c))/(3abc) is a/(3c)+b/(3c)+b/(3a)+c/(3a)+a/(3b)+c/(3b)