If ab minus 1 b cb minus 1 c ac minus 1 a then find the value of a c b a c b ........

Quantitative Aptitude ( CCS) Algebra

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If (ab−1)/b=(cb−1)/c=(ac−1)a, then find the value of (a/c+b/a+c/b)

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Explanation:

Taking, (ab - 1)/b = (cb - 1)/c
⇒ abc - c = cb²- b
⇒ cb² = abc + b - c ----(1)
Taking, (ab - 1)/b = (ac - 1)/a
⇒ a²b - a = abc - b
⇒ a²b = abc + a - b ----(2)
Taking, (cb - 1)/c = (ac - 1)/a
⇒ abc - a = ac2 - c
⇒ ac² = abc + c - a ----(3)
∴ a/c + b/a + c/b
= (a²b + b²c + c²a)/abc
Substituting from (1), (2) & (3),
= (abc + a - b + abc + b - c + abc + c - a)/abc
= 3abc/abc
= 3