If (a+b):(b+c):(c+a)=5:7:6, then what is the value of (a-b+c):(a+b-c)?

Explanation

Let a+b=5k, b+c=7k, and c+a=6k. Adding all three equations gives 2(a+b+c) = 18k, which simplifies to a+b+c = 9k. From this, we can find individual values: c = 9k - 5k = 4k, a = 9k - 7k = 2k, and b = 9k - 6k = 3k. Substituting these into the required ratio gives (2k-3k+4k) : (2k+3k-4k) = 3k : 1k = 3:1.

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