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jmc

algebra senior

Problem

Solve for

n

:

\frac{2 - n}{n + 1} + \frac{2 n - 4}{2 - n} = 1

.

Solution

Note that

\frac{2 n - 4}{2 - n} = \frac{2 ( n - 2 )}{- ( n - 2 )} = - 2

. From this, we can rewrite the given equation and solve:

\frac{2 - n}{n + 1} - 2 \Rightarrow \frac{2 - n}{n + 1} \Rightarrow 2 - n \Rightarrow - 1 \Rightarrow - \frac{1}{4} = 1 = 3 = 3 n + 3 = 4 n = n

Final answer

-\frac{1}{4}