For x≠0, 1x+12x+13x equals

1981 AMC 12 Problem 3

Attempt Problem 3 of the 1981 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1981 AMC 12 solutions, or check the answer key.

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For

x\ne0,

\frac1x+\frac1{2x}+\frac1{3x}

equals

\frac1{2x}

\frac1{6x}

\frac5{6x}

\frac{11}{6x}

\frac1{6x^3}

Use

6x

as a common denominator

Add the resulting numerators

6,

3,

and

2

Using the common denominator

6x

gives

\begin{aligned} \frac1x+\frac1{2x}+\frac1{3x} &=\frac6{6x}+\frac3{6x}\\ &\quad+\frac2{6x}\\ &=\frac{11}{6x}. \end{aligned}

Therefore, the correct answer is D.