Problem

$1 \leftarrow$ Solve $\frac{1}{A}=\frac{1}{v}+\frac{1}{p}$ for $p$

Answer

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Answer

So, the solution to the equation \(\frac{1}{A}=\frac{1}{v}+\frac{1}{p}\) for \(p\) is \(\boxed{p = \frac{Av}{A - v}}\).

Steps

Step 1 ：Start with the equation \(\frac{1}{A}=\frac{1}{v}+\frac{1}{p}\).

Step 2 ：Subtract \(\frac{1}{v}\) from both sides to get \(\frac{1}{p} = \frac{1}{A} - \frac{1}{v}\).

Step 3 ：Take the reciprocal of both sides to isolate \(p\), giving \(p = \frac{1}{\frac{1}{A} - \frac{1}{v}}\).

Step 4 ：Simplify the right side of the equation to get \(p = \frac{Av}{A - v}\).

Step 5 ：So, the solution to the equation \(\frac{1}{A}=\frac{1}{v}+\frac{1}{p}\) for \(p\) is \(\boxed{p = \frac{Av}{A - v}}\).

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