Solve for R1 i=V/(R_1+R_2)

$i = \frac{V}{R_{1} + R_{2}}$

Step 1

Multiply both sides by $R_{1} + R_{2}$ .

$i (R_{1} + R_{2}) = \frac{V}{R_{1} + R_{2}} (R_{1} + R_{2})$

Step 2

Simplify.

Simplify the left side.

Simplify $i (R_{1} + R_{2})$ .

Apply the distributive property.

$i R_{1} + i R_{2} = \frac{V}{R_{1} + R_{2}} (R_{1} + R_{2})$

Simplify with commuting.

Reorder $i$ and $R_{1}$ .

$R_{1} i + i R_{2} = \frac{V}{R_{1} + R_{2}} (R_{1} + R_{2})$

Reorder $i$ and $R_{2}$ .

$R_{1} i + R_{2} i = \frac{V}{R_{1} + R_{2}} (R_{1} + R_{2})$

Simplify the right side.

Cancel the common factor of $R_{1} + R_{2}$ .

Cancel the common factor.

$R_{1} i + R_{2} i = \frac{V}{R_{1} + R_{2}} (R_{1} + R_{2})$

Rewrite the expression.

$R_{1} i + R_{2} i = V$

Step 3

Rewrite the equation as $V = R_{1} i + R_{2} i$ .

$V = R_{1} i + R_{2} i$