Question

Solve  StartFraction 1 Over Upper A EndFraction equals StartFraction 1 Over n EndFraction plus StartFraction 1 Over w EndFraction
for w.

Answer 1

To solve the equation

\[
\frac{1}{A} = \frac{1}{n} + \frac{1}{w}
\]

for \(w\), we will first isolate \( \frac{1}{w} \).

1. Rearrange the equation:

\[
\frac{1}{w} = \frac{1}{A} - \frac{1}{n}
\]

2. To combine the fractions on the right side, find a common denominator. The common denominator of \(A\) and \(n\) is \(An\):

\[
\frac{1}{w} = \frac{n}{An} - \frac{A}{An}
\]

3. Combine the fractions:

\[
\frac{1}{w} = \frac{n - A}{An}
\]

4. Now, take the reciprocal of both sides to solve for \(w\):

\[
w = \frac{An}{n - A}
\]

Thus, the solution for \(w\) is:

\[
w = \frac{An}{n - A}
\]