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algebra intermediate

Problem

If

x = 1 + 2^{p}

and

y = 1 + 2^{- p}

, then

y

in terms of

x

is

(A)

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

(B)

\frac{x + 2}{x - 1}

(C)

\frac{x}{x - 1}

(D)

2 - x

Solution

Since we want the

y

expression in terms of

x

, let's convert the

y

expression. We can convert it to

1 + \frac{1}{2 ^{p}} \Rightarrow \frac{2 ^{p} + 1}{2 ^{p}} \Rightarrow \frac{x}{x - 1} \Rightarrow

\frac{x}{x - 1}

Final answer

C