To solve the formula \( \frac{E}{e} = \frac{R + r}{R} \) for \( e \), follow these steps.
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Start with the equation: \[ \frac{E}{e} = \frac{R + r}{R} \]
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Multiply both sides by \( e \) to eliminate the fraction on the left: \[ E = e \cdot \frac{R + r}{R} \]
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Next, solve for \( e \) by isolating it on one side. To do this, divide both sides by \( \frac{R + r}{R} \): \[ e = \frac{E}{\frac{R + r}{R}} \]
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To simplify the right side, multiply by the reciprocal: \[ e = E \cdot \frac{R}{R + r} \]
Thus, the solution for \( e \) is: \[ e = \frac{E \cdot R}{R + r} \]