# Difference between revisions of "1976 AHSME Problems/Problem 1"

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− | The reciprocal of <math>(1-x)</math> is <math>\frac{1}{1-x}</math>, so our equation is <cmath>1-\frac{1}{1-x}=\frac{1}{1-x},</cmath> which is equivalent to <math>\frac{1}{1-x}=\frac{1}{2}</math>. So, <math>1-x=2</math> and <math>x=-2\Rightarrow \textbf{(A)}</math>. | + | The reciprocal of <math>(1-x)</math> is <math>\frac{1}{1-x}</math>, so our equation is <cmath>1-\frac{1}{1-x}=\frac{1}{1-x},</cmath> which is equivalent to <math>\frac{1}{1-x}=\frac{1}{2}</math>. So, <math>1-x=2</math> and <math>x=-2\Rightarrow \textbf{(A)}</math>.~MathJams |

## Revision as of 20:48, 11 July 2020

## Problem 1

If one minus the reciprocal of equals the reciprocal of , then equals

## Solution

The reciprocal of is , so our equation is which is equivalent to . So, and .~MathJams