#### Question

If `(a + b)/(am + bn)= (b + c)/(mb + nc )= (c + a)/(mc + na)` prove that each of theseccc `2/(m+n)`provided a + b + c ≠ 0

#### Solution

`(a + b)/(am + bn)= (b + c)/(mb + nc )= (c + a)/(mc + na)` `

`" sumof antecedents"/"sumof consequents"`

= `(a + b+b+c+c+a)/(am + bn +mb+ nc +mc+na)`

= `(2(a+b+c))/(m(a+b+c) =n (a+b+c))`

= `2/(m+n)`

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Solution If `(A + B)/(Am + Bn)= (B + C)/(Mb + Nc )= (C + A)/(Mc + Na)` Prove that Each of These Ratios is Equal to `2/(M+N)`Provided a + B + C ≠ 0 Concept: Ratio and Proportion Example.