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1980 AHSME Problems/Problem 8

Revision as of 12:11, 16 July 2012 by Mrdavid445 (talk | contribs) (Created page with "==Problem== How many pairs <math>(a,b)</math> of non-zero real numbers satisfy the equation <cmath> \frac{1}{a} + \frac{1}{b} = \frac{1}{a+b} </cmath> <math>\text{(A)} \ \text...")
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Problem

How many pairs $(a,b)$ of non-zero real numbers satisfy the equation

\[\frac{1}{a} + \frac{1}{b} = \frac{1}{a+b}\] $\text{(A)} \ \text{none} \qquad \text{(B)} \ 1 \qquad \text{(C)} \ 2 \qquad \text{(D)} \ \text{one pair for each} ~b \neq 0$ $\text{(E)} \ \text{two pairs for each} ~b \neq 0$

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