Solve for R F=w/(2R)*(R-r)

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

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.

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

$2 R, 1, 1$

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.

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

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

Simplify the left side.

Rewrite using the commutative property of multiplication.

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

Cancel the common factor of $2$ .

Factor $2$ out of $2 R$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Cancel the common factor of $R$ .

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Simplify the right side.

Rewrite using the commutative property of multiplication.

$w R - w r = 2 F R$

Step 4

Solve the equation.

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

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

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

$w R - 2 F R = w r$

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

Factor $R$ out of $w R$ .

$R w - 2 F R = w r$

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

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

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

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

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

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

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

Simplify the left side.

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

Cancel the common factor.

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

Divide $R$ by $1$ .

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

Solve for R F=w/(2R)*(R-r)

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