Question

a+b+c=12 and 1/(a+b)+1/(b+c)+1/(a+c)=5/6 find c/(a+b)+a/(b+c)+b/(a+c)​

Answer 1

Answer:

7

Step-by-step explanation:

c/(a+b)+a/(b+c)+b/(a+c) = ( c/(a+b)+a/(b+c)+b/(a+c) ) +1+1+1 -1-1-1

= ( c/(a+b) +1 +a/(b+c) + 1 + b/(a+c) +1 ) -1-1-1

= ( (a+b+c)/(a+b) + (a+b+c)/(b+c) + (a+b+c)/(a+c) ) -3

= [ (a+b+c){ 1/(a+b)+1/(b+c)+1/(a+c) } ] -3

By putting the given value,

= 12 × 5/6 - 3

= 10 - 3 = 7

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