(r)/(m) = (1)/(x) + (1)/(P)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution for the equation:
$$\frac{r}{m} = \frac{1}{x} + \frac{1}{P}$$
The goal is to express $x$ in terms of $r$, $m$, and $P$.
Step 1: Isolate the term containing $x$. Subtract $\frac{1}{P}$ from both sides of the equation.
$$\frac{r}{m} - \frac{1}{P} = \frac{1}{x}$$
Step 2: Combine the terms on the left side into a single fraction. The least common denominator for $m$ and $P$ is $mP$.
$$\frac{r \cdot P}{m \cdot P} - \frac{1 \cdot m}{P \cdot m} = \frac{1}{x}$$
$$\frac{rP}{mP} - \frac{m}{mP} = \frac{1}{x}$$
$$\frac{rP - m}{mP} = \frac{1}{x}$$
Step 3: Invert both sides of the equation to solve for $x$.
$$x = \frac{mP}{rP - m}$$
The solution for $x$ in terms of $r$, $m$, and $P$ is:
$$\boxed{x = \frac{mP}{rP - m}}$$
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