Question

Найдите ab/c, если ab/(a+b)=1; ac/(a+c)=2; bc/(b+c)=3.

Answer 1

 
 $frac{ab}{a+b}=1\ frac{1}{frac{a+b}{ab}}=1 \ frac{a+b}{ab}=1\ frac{1}{a}+frac{1}{b}=1\ \ frac{ac}{a+c}=2\ frac{1}{frac{a+c}{ac}}=2\ frac{a+c}{ac}=frac{1}{2}\ frac{1}{a}+frac{1}{c} \\ frac{bc}{b+c}=3 \ frac{1}{b}+frac{1}{c}=frac{1}{3}$
$frac{1}{a}+frac{1}{b}=1\ frac{1}{a}+frac{1}{c}=frac{1}{2}\ frac{1}{b}+frac{1}{c }=frac{1}{3}\\ frac{1}{b}-frac{1}{c}=frac{1}{2}\ frac{1}{b}+frac{1}{c}=frac{1}{3}\\ frac{2}{b}=frac{5}{6}\ b=frac{12}{5}\ c=-12 \ a=frac{12}{7}\ frac{ab}{c}=frac{-12}{35}$