Algebra Examples

$I = \frac{R - U}{S}$

Step 1

Solve the equation for $U$ .

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Rewrite the equation as $\frac{R - U}{S} = I$ .

$\frac{R - U}{S} = I$

Multiply both sides by $S$ .

$\frac{R - U}{S} S = I S$

Simplify the left side.

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Cancel the common factor of $S$ .

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Cancel the common factor.

$\frac{R - U}{S} S = I S$

Rewrite the expression.

$R - U = I S$

Solve for $U$ .

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Subtract $R$ from both sides of the equation.

$- U = I S - R$

Divide each term in $- U = I S - R$ by $- 1$ and simplify.

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Divide each term in $- U = I S - R$ by $- 1$ .

$\frac{- U}{- 1} = \frac{I S}{- 1} + \frac{- R}{- 1}$

Simplify the left side.

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Dividing two negative values results in a positive value.

$\frac{U}{1} = \frac{I S}{- 1} + \frac{- R}{- 1}$

Divide $U$ by $1$ .

$U = \frac{I S}{- 1} + \frac{- R}{- 1}$

Simplify the right side.

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Simplify each term.

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Move the negative one from the denominator of $\frac{I S}{- 1}$ .

$U = - 1 \cdot (I S) + \frac{- R}{- 1}$

Rewrite $- 1 \cdot (I S)$ as $- (I S)$ .

$U = - (I S) + \frac{- R}{- 1}$

Dividing two negative values results in a positive value.

$U = - I S + \frac{R}{1}$

Divide $R$ by $1$ .

$U = - I S + R$

Step 2

Solve the equation for $S$ .

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Rewrite the equation as $\frac{R - (- I S + R)}{S} = I$ .

$\frac{R - (- I S + R)}{S} = I$

Factor each term.

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Apply the distributive property.

$\frac{R - (- I S) - R}{S} = I$

Multiply $- (- I S)$ .

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Multiply $- 1$ by $- 1$ .

$\frac{R + 1 (I S) - R}{S} = I$

Multiply $I$ by $1$ .

$\frac{R + I S - R}{S} = I$

Subtract $R$ from $R$ .

$\frac{I S + 0}{S} = I$

Add $I S$ and $0$ .

$\frac{I S}{S} = I$

Reduce the expression by cancelling the common factors.

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Reduce the expression $\frac{I S}{S}$ by cancelling the common factors.

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Cancel the common factor.

$\frac{I S}{S} = I$

Rewrite the expression.

$\frac{I}{1} = I$

Divide $I$ by $1$ .

$I = I$

Solve the equation.

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Move all terms containing $I$ to the left side of the equation.

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Subtract $I$ from both sides of the equation.

$I - I = 0$

Subtract $I$ from $I$ .

$0 = 0$

Since $0 = 0$ , the equation will always be true.

Always true