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Prove that f(a, b, c) = 4 max {1/a, 1/b, 1/c}

Source:

9/29/2010
Let a,b,ca,b,c be reals and f(a,b,c)=∣∣b−a∣∣ab∣+b+aab−2c∣+∣b−a∣∣ab∣+b+aab+2cf(a, b, c) = \left| \frac{ |b-a|}{|ab|} +\frac{b+a}{ab} -\frac 2c \right| +\frac{ |b-a|}{|ab|} +\frac{b+a}{ab} +\frac 2c Prove that f(a,b,c)=4max⁡{1a,1b,1c}.f(a, b, c) = 4 \max \{\frac 1a, \frac 1b,\frac 1c \}.
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