The arithmetic mean between (x+a)/(x) and (x-a)/(x), when x≠0, is:

1958 AMC 12 Problem 6

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The arithmetic mean between

\dfrac{x+a}{x}

and

\dfrac{x-a}{x},

when

x\ne0,

is:

2,

a\ne0

1

1,

only if

a=0

\dfrac ax

x

Add the two given expressions and divide by

2

The

a

-terms cancel in the numerator

The arithmetic mean is

\begin{aligned} &\frac12\left(\frac{x+a}{x}+\frac{x-a}{x}\right)\\ &\qquad=\frac12\left(\frac{2x}{x}\right)=1. \end{aligned}

Therefore, the correct answer is B.