How do you solve for e in #E/e=(R+r)/r#?

Question

Savannah Anderson · Accepted Answer

#e=(rE)/(R+r)#

Given:#" "E/e=(R+r)/r#

Applying fundamental principles:

#color(blue)("YOU CAN DO THIS:"->"Turn everything upside down giving:")#

#color(green)(e/E=r/(R+r))#

Add E to both sides.

#color(green)(e/Ecolor(red)(xxE)" "=" "r/(R+r)color(red)(xxE))#

#color(green)(e xx(color(red)(E))/E" "=" "(rE)/(R+r)#

But #E/E=1# and #1xxe=e#

#e=(rE)/(R+r)#

Eli Assouline · Answer

undefined To solve for $ e $ in the equation $ \frac{E}{e} = \frac{R+r}{r} $, you can first multiply both sides of the equation by $ e $ to eliminate the fraction. Then, rearrange the terms to isolate $ e $ on one side of the equation. The steps are as follows:

1. Multiply both sides by $ e $:
$$ e \times \frac{E}{e} = e \times \frac{R+r}{r} $$

2. Simplify:
$$ E = \frac{e(R+r)}{r} $$

3. Multiply both sides by $ r $ to eliminate the denominator:
$$ Er = e(R+r) $$

4. Expand the right side:
$$ Er = eR + er $$

5. Move all terms containing $ e $ to one side and other terms to the other side:
$$ Er - eR = er $$

6. Factor out $ e $ on the left side:
$$ e(R - R) = er $$

7. Simplify:
$$ e \cdot 0 = er $$

8. Since $ e \cdot 0 = 0 $, we have:
$$ 0 = er $$

9. Divide both sides by $ r $ to solve for $ e $:
$$ \frac{0}{r} = \frac{er}{r} $$

$$ 0 = e $$

Therefore, $ e = 0 $.