Here is the solution for the equation: r/m = 1/x + 1/P The goal is to express x in terms of r, m, and P. Step 1: Isolate the term containing x. Subtract 1/P from both sides of the equation. r/m − 1/P = 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. (r · P)/(m · P) − (1 · m)/(P · m) = 1/x; rP/mP − m/mP = 1/x; (rP − m)/(mP) = 1/x Step 3: Invert both sides of the equation to solve for x. x = (mP)/(rP − m) The solution for x in terms of r, m, and P is: x = (mP)/(rP − m)

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/(m) = (1)/(x) + (1)/(P)

April 18, 2026Mathematics

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Answer

x = \frac{mP}{rP - m}

Step-by-step solution

3 steps

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 $P$ .

Isolate the term containing $x$ .
Subtract $\frac{1}{P}$ from both sides of the equation.
$\frac{r}{m} - \frac{1}{P} = \frac{1}{x}$
Combine the terms on the left side into a single fraction.
The least common denominator for $m$ and $P$ is $mP$ .
$\frac{r \cdot P}{m \cdot P} - \frac{1 \cdot m}{P \cdot m} = \frac{1}{x}$ $\frac{rP}{mP} - \frac{m}{mP} = \frac{1}{x}$ $\frac{rP - m}{mP} = \frac{1}{x}$
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:

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/(m) = (1)/(x) + (1)/(P)

Answer

Step-by-step solution

Isolate the term containing xxx.

Combine the terms on the left side into a single fraction.

Invert both sides of the equation to solve for xxx.

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More Mathematics Questions

Isolate the term containing $x$ .

Invert both sides of the equation to solve for $x$ .