Basic Math Examples

$F = \frac{w}{2 R} \cdot (R - r)$

Step 1

Rewrite the equation as $\frac{w}{2 R} \cdot (R - r) = F$ .

$\frac{w}{2 R} \cdot (R - r) = F$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 R, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 R$

Step 3

Multiply each term in $\frac{w}{2 R} \cdot (R - r) = F$ by $2 R$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{w}{2 R} \cdot (R - r) = F$ by $2 R$ .

$\frac{w}{2 R} \cdot (R - r) (2 R) = F (2 R)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{w}{2 R} (R - r) R = F (2 R)$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $2 R$ .

$2 \frac{w}{2 (R)} (R - r) R = F (2 R)$

Step 3.2.2.2

Cancel the common factor.

$2 \frac{w}{2 R} (R - r) R = F (2 R)$

Step 3.2.2.3

Rewrite the expression.

$\frac{w}{R} (R - r) R = F (2 R)$

Step 3.2.3

Multiply $\frac{w}{R}$ by $R - r$ .

$\frac{w (R - r)}{R} R = F (2 R)$

Step 3.2.4

Cancel the common factor of $R$ .

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Step 3.2.4.1

Cancel the common factor.

$\frac{w (R - r)}{R} R = F (2 R)$

Step 3.2.4.2

Rewrite the expression.

$w (R - r) = F (2 R)$

Step 3.2.5

Apply the distributive property.

$w R + w (- r) = F (2 R)$

Step 3.2.6

Rewrite using the commutative property of multiplication.

$w R - w r = F (2 R)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite using the commutative property of multiplication.

$w R - w r = 2 F R$

Step 4

Solve the equation.

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Step 4.1

Subtract $2 F R$ from both sides of the equation.

$w R - w r - 2 F R = 0$

Step 4.2

Add $w r$ to both sides of the equation.

$w R - 2 F R = w r$

Step 4.3

Factor $R$ out of $w R - 2 F R$ .

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Step 4.3.1

Factor $R$ out of $w R$ .

$R w - 2 F R = w r$

Step 4.3.2

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

$R w + R (- 2 F) = w r$

Step 4.3.3

Factor $R$ out of $R w + R (- 2 F)$ .

$R (w - 2 F) = w r$

Step 4.4

Divide each term in $R (w - 2 F) = w r$ by $w - 2 F$ and simplify.

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Step 4.4.1

Divide each term in $R (w - 2 F) = w r$ by $w - 2 F$ .

$\frac{R (w - 2 F)}{w - 2 F} = \frac{w r}{w - 2 F}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $w - 2 F$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{R (w - 2 F)}{w - 2 F} = \frac{w r}{w - 2 F}$

Step 4.4.2.1.2

Divide $R$ by $1$ .

$R = \frac{w r}{w - 2 F}$