1976 AMC 12 Problem 1

Attempt Problem 1 of the 1976 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 1976 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

If one minus the reciprocal of

(1-x)

equals the reciprocal of

(1-x),

then

x

equals

-2

-1

\frac12

2

3

Multiply the equation by

1-x,

which cannot be zero

After clearing the denominator, solve

1-x-1=1

The equation is

1-\frac1{1-x}=\frac1{1-x}.

Multiplying by

1-x\ne0

gives

1-x-1=1,

x=-1.

Therefore, the correct answer is B.

Problem 1 in other years