Solve for R i=a/R

$i = \frac{a}{R}$

Step 1

Rewrite the equation as $\frac{a}{R} = i$ .

$\frac{a}{R} = i$

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.

$R, 1$

The LCM of one and any expression is the expression.

$R$

Step 3

Multiply each term in $\frac{a}{R} = i$ by $R$ to eliminate the fractions.

Multiply each term in $\frac{a}{R} = i$ by $R$ .

$\frac{a}{R} R = i R$

Simplify the left side.

Cancel the common factor of $R$ .

Cancel the common factor.

$\frac{a}{R} R = i R$

Rewrite the expression.

$a = i R$

Step 4

Solve the equation.

Rewrite the equation as $i R = a$ .

$i R = a$

Divide each term in $i R = a$ by $i$ and simplify.

Divide each term in $i R = a$ by $i$ .

$\frac{i R}{i} = \frac{a}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i R}{i} = \frac{a}{i}$

Divide $R$ by $1$ .

$R = \frac{a}{i}$

Simplify the right side.

Multiply the numerator and denominator of $\frac{a}{i}$ by the conjugate of $i$ to make the denominator real.

$R = \frac{a}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$R = \frac{a i}{i i}$

Simplify the denominator.

Raise $i$ to the power of $1$ .

$R = \frac{a i}{i^{1} i}$

Raise $i$ to the power of $1$ .

$R = \frac{a i}{i^{1} i^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$R = \frac{a i}{i^{1 + 1}}$

Add $1$ and $1$ .

$R = \frac{a i}{i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$R = \frac{a i}{- 1}$

Move the negative one from the denominator of $\frac{a i}{- 1}$ .

$R = - 1 \cdot (a i)$

Rewrite $- 1 \cdot (a i)$ as $- (a i)$ .

$R = - a i$

Solve for R i=a/R

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