Question

practice: solve rational equations
score: 5/6 answered: 5/6
question 6
solve the equation for the specified variable.
$i = \frac{v}{r + r}$
$r = \square$

Explanation:

Step1: Multiply both sides by \( R + r \)

To eliminate the denominator, we multiply both sides of the equation \( I = \frac{V}{R + r} \) by \( R + r \). This gives us \( I(R + r) = V \).

Step2: Distribute \( I \) on the left side

Using the distributive property, we expand the left side: \( IR + Ir = V \).

Step3: Subtract \( IR \) from both sides

To isolate the term with \( r \), we subtract \( IR \) from both sides: \( Ir = V - IR \).

Step4: Divide both sides by \( I \)

Finally, we divide both sides by \( I \) to solve for \( r \): \( r = \frac{V - IR}{I} \), which can also be written as \( r = \frac{V}{I} - R \).

Answer:

\( \frac{V}{I} - R \) (or \( \frac{V - IR}{I} \))