Solve for r I=E/(R+r) for r

$I = \frac{E}{R + r}$ for $r$

Step 1

Rewrite the equation as $\frac{E}{R + r} = I$ .

$\frac{E}{R + r} = I$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$R + r, 1$

Remove parentheses.

$R + r, 1$

The LCM of one and any expression is the expression.

$R + r$

Step 3

Multiply each term in $\frac{E}{R + r} = I$ by $R + r$ to eliminate the fractions.

Multiply each term in $\frac{E}{R + r} = I$ by $R + r$ .

$\frac{E}{R + r} (R + r) = I (R + r)$

Simplify the left side.

Cancel the common factor of $R + r$ .

Cancel the common factor.

$\frac{E}{R + r} (R + r) = I (R + r)$

Rewrite the expression.

$E = I (R + r)$

Simplify the right side.

Apply the distributive property.

$E = I R + I r$

Step 4

Solve the equation.

Rewrite the equation as $I R + I r = E$ .

$I R + I r = E$

Subtract $I R$ from both sides of the equation.

$I r = E - I R$

Divide each term in $I r = E - I R$ by $I$ and simplify.

Divide each term in $I r = E - I R$ by $I$ .

$\frac{I r}{I} = \frac{E}{I} + \frac{- I R}{I}$

Simplify the left side.

Cancel the common factor of $I$ .

Cancel the common factor.

$\frac{I r}{I} = \frac{E}{I} + \frac{- I R}{I}$

Divide $r$ by $1$ .

$r = \frac{E}{I} + \frac{- I R}{I}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $I$ .

Cancel the common factor.

$r = \frac{E}{I} + \frac{- I R}{I}$

Divide $- 1 R$ by $1$ .

$r = \frac{E}{I} - 1 R$

Rewrite $- 1 R$ as $- R$ .

$r = \frac{E}{I} - R$

Solve for r I=E/(R+r) for r

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