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

Найдем a * b/c, если a * b/(a + b) = 1; a * c/(a + c) = 2; b * c/(b + c) = 3. 

Решим систему уравнений: 

{ a * b/(a + b) = 1; 

a * c/(a + c) = 2; 

b * c/(b + c) = 3; 

1) a * b/(a + b) = 1; 

a * b = a + b; 

a * b - a = b; 

a * (b - 1) = b; 

a = b/(b - 1); 

2) a * c/(a + c) = 2; 

a * c = 2 * a + 2 * c; 

a * c - 2 * c = 2 * a; 

c = 2 * a/(a - 2); 

c = 2 * (b/(b - 1))/( b/(b - 1) - 2); 

c = 2 * b/(b - 1)/((b - 2 * (b - 1))/(b - 1)); 

c = 2 * b/(b - 1)/((b - 2 * b + 2)/(b - 1)); 

c = 2 * b/(b - 1) * (b - 1)/(2 - b); 

c = 2 * b/(2 - b); 

3) b * c/(b + c) = 3;  

(b * 2 * b/(2 - b))/(b + 2 * b/(2 - b)) = 3; 

(2 * b^2/(2 - b))/((b * (2 - b) + 2 * b)/(2 - b)) = 3;  

(2 * b^2/(2 - b))/((2 * b - b^2 + 2 * b)/(2 - b)) = 3; 

(2 * b^2/(2 - b)) * (2 - b)/(4 * b - b^2) = 3; 

2 * b^2/(4 * b * b^2) = 3; 

2 * b/(4 - b) = 3; 

3 * (4 - b) = 2 * b; 

12 - 3 * b = 2 * b; 

12 = 5 * b; 

b = 2.4; 

4) a = b/(b - 1) = 2.4/(2.4 - 1) = 2.4/1.4 = 24/14 = 12/7; 

5) c = 2 * b/(2 - b) = 2 * 12/7/(2 - 12/7) = 24/7/(2/7) = 24/7 * 7/2 = 24/2 = 12. 

Теперь найдем значение выражения a * b/c: 

a * b/c = 12/7 * 2.4/12 = 12 * 2.4/(7 * 12) = 2.4/7 = (2 4/10)/7 = (2 2/5)/7 = (12/5)/7 = 12/5 * 1/7 = 12/35.