If x=(a)/(b), a≠ b, and b≠0, then (a+b)/(a-b)=

1991 AMC 12 Problem 7

Attempt Problem 7 of the 1991 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 1991 AMC 12 solutions, or check the answer key.

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x=\frac{a}{b},

a\ne b,

and

b\ne0,

then

\dfrac{a+b}{a-b}=

\frac{x}{x+1}

\frac{x+1}{x-1}

1

x-\frac1x

x+\frac1x

Divide the numerator and denominator by

b

Replace each occurrence of

\frac{a}{b}

x

Dividing both numerator and denominator by the nonzero number

b

gives

\frac{a+b}{a-b}=\frac{\frac{a}{b}+1}{\frac{a}{b}-1}=\frac{x+1}{x-1}.

Thus the correct answer is B.