Make $$ m $$ the subject of the fol $$ I=\frac{n e}{R+\frac{n r}{m}} $$

Question

UpStudy AI · Accepted Answer

To make $$ m $$ the subject of the equation

$$
I = \frac{n e}{R + \frac{n r}{m}},
$$

follow these steps:

1. **Start with the given equation:**

$$
   I = \frac{n e}{R + \frac{n r}{m}}.
   $$

2. **Invert both sides to eliminate the fraction:**

$$
   \frac{1}{I} = \frac{R + \frac{n r}{m}}{n e}.
   $$

3. **Multiply both sides by $$ n e $$ to isolate the denominator:**

$$
   \frac{n e}{I} = R + \frac{n r}{m}.
   $$

4. **Subtract $$ R $$ from both sides to isolate the term containing $$ m $$:**

$$
   \frac{n e}{I} - R = \frac{n r}{m}.
   $$

5. **Multiply both sides by $$ m $$ to solve for $$ m $$:**

$$
   m \left( \frac{n e}{I} - R \right) = n r.
   $$

6. **Finally, solve for $$ m $$:**

$$
   m = \frac{n r}{\frac{n e}{I} - R}.
   $$

To simplify the expression further, you can multiply the numerator and the denominator by $$ I $$:

$$
   m = \frac{n r I}{n e - R I}.
   $$

**Final Expression:**

$$
m = \frac{n r I}{n e - R I}
$$

This equation now expresses $$ m $$ in terms of $$ I $$, $$ n $$, $$ e $$, $$ R $$, and $$ r $$.

**Answer in LaTeX:**

After rearranging, the solution for $$ m $$ is

$$
m = \frac{n r\, I}{n e - R I}
$$
$$ m = \frac{n r\, I}{n e - R I} $$

Make the subject of the fol