\(\frac{E}{e}=\frac{R+r}{R-r}\)
Multiply both sides of the equation by (R - r) .
\((R-r)\,*\,\frac{E}{e}=R+r\)
Distribute the \( \frac{E}{e} \) .
\(R*\frac{E}{e}\,-\,r*\frac{E}{e}=R+r\)
Add \( r*\frac{E}{e} \) to both sides of the equation.
\(R*\frac{E}{e}=R+r+r*\frac{E}{e}\)
Subtract R from both sides of the equation.
\(R*\frac{E}{e}-R=r+r*\frac{E}{e}\)
Factor out an r on the right side.
\(R*\frac{E}{e}-R=r(1+\frac{E}{e})\)
Divide both sides of the equation by \( (1+\frac{E}{e}) \) .
\(\frac{R*\frac{E}{e}-R}{1+\frac{E}{e}}=r\)
\(\frac{E}{e}=\frac{R+r}{R-r}\)
Multiply both sides of the equation by (R - r) .
\((R-r)\,*\,\frac{E}{e}=R+r\)
Distribute the \( \frac{E}{e} \) .
\(R*\frac{E}{e}\,-\,r*\frac{E}{e}=R+r\)
Add \( r*\frac{E}{e} \) to both sides of the equation.
\(R*\frac{E}{e}=R+r+r*\frac{E}{e}\)
Subtract R from both sides of the equation.
\(R*\frac{E}{e}-R=r+r*\frac{E}{e}\)
Factor out an r on the right side.
\(R*\frac{E}{e}-R=r(1+\frac{E}{e})\)
Divide both sides of the equation by \( (1+\frac{E}{e}) \) .
\(\frac{R*\frac{E}{e}-R}{1+\frac{E}{e}}=r\)
Good work Hectictar :)
There is no way I could read this question, it was just too small.
Solve for r:
E/e = (r + R)/(R - r)
E/e = (r + R)/(R - r) is equivalent to (r + R)/(R - r) = E/e:
(r + R)/(R - r) = E/e
Cross multiply:
e (r + R) = E (R - r)
Expand out terms of the left hand side:
e r + e R = E (R - r)
Expand out terms of the right hand side:
e r + e R = E R - E r
Subtract e R - E r from both sides:
r (E + e) = E R - e R
Divide both sides by E + e:
Answer: | r = (E R - e R)/(E + e)=R[E - e] / [E + e]