Algebra Examples

$R = \frac{2 A S}{L - 2 S}$

Step 1

Rewrite the equation as $\frac{2 A S}{L - 2 S} = R$ .

$\frac{2 A S}{L - 2 S} = R$

Step 2

Multiply both sides by $L - 2 S$ .

$\frac{2 A S}{L - 2 S} (L - 2 S) = R (L - 2 S)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $L - 2 S$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{2 A S}{L - 2 S} (L - 2 S) = R (L - 2 S)$

Step 3.1.1.2

Rewrite the expression.

$2 A S = R (L - 2 S)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $R (L - 2 S)$ .

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Step 3.2.1.1

Apply the distributive property.

$2 A S = R L + R (- 2 S)$

Step 3.2.1.2

Simplify the expression.

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Step 3.2.1.2.1

Rewrite using the commutative property of multiplication.

$2 A S = R L - 2 R S$

Step 3.2.1.2.2

Reorder $R$ and $L$ .

$2 A S = L R - 2 R S$

Step 4

Divide each term in $2 A S = L R - 2 R S$ by $2 S$ and simplify.

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Step 4.1

Divide each term in $2 A S = L R - 2 R S$ by $2 S$ .

$\frac{2 A S}{2 S} = \frac{L R}{2 S} + \frac{- 2 R S}{2 S}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 A S}{2 S} = \frac{L R}{2 S} + \frac{- 2 R S}{2 S}$

Step 4.2.1.2

Rewrite the expression.

$\frac{A S}{S} = \frac{L R}{2 S} + \frac{- 2 R S}{2 S}$

Step 4.2.2

Cancel the common factor of $S$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{A S}{S} = \frac{L R}{2 S} + \frac{- 2 R S}{2 S}$

Step 4.2.2.2

Divide $A$ by $1$ .

$A = \frac{L R}{2 S} + \frac{- 2 R S}{2 S}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Cancel the common factor of $- 2$ and $2$ .

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Step 4.3.1.1.1

Factor $2$ out of $- 2 R S$ .

$A = \frac{L R}{2 S} + \frac{2 (- R S)}{2 S}$

Step 4.3.1.1.2

Cancel the common factors.

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Step 4.3.1.1.2.1

Factor $2$ out of $2 S$ .

$A = \frac{L R}{2 S} + \frac{2 (- R S)}{2 (S)}$

Step 4.3.1.1.2.2

Cancel the common factor.

$A = \frac{L R}{2 S} + \frac{2 (- R S)}{2 S}$

Step 4.3.1.1.2.3

Rewrite the expression.

$A = \frac{L R}{2 S} + \frac{- R S}{S}$

Step 4.3.1.2

Cancel the common factor of $S$ .

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Step 4.3.1.2.1

Cancel the common factor.

$A = \frac{L R}{2 S} + \frac{- R S}{S}$

Step 4.3.1.2.2

Divide $- R$ by $1$ .

$A = \frac{L R}{2 S} - R$