x/a+x/b+x/c =1

解

\frac{x}{a} + \frac{x}{b} + \frac{x}{c} = 1

x = \frac{ab c}{b c + a c + ab}; ab c \neq = 0, a \neq = - \frac{b c}{c + b}

解答ステップ

\frac{x}{a} + \frac{x}{b} + \frac{x}{c} = 1

LCMで乗じる

b c x + a c x + ab x = ab c; ab c \neq = 0

因数

b c x + a c x + ab x : x (b c + a c + ab)

x (b c + a c + ab) = ab c; ab c \neq = 0

以下で両辺を割る

b c + a c + ab; ab c \neq = 0, a \neq = - \frac{b c}{c + b}

x = \frac{ab c}{b c + a c + ab}; ab c \neq = 0, a \neq = - \frac{b c}{c + b}