Solve for R W=(2PR)/(R-r)

$W = \frac{2 P R}{R - r}$

Rewrite the equation as $\frac{2 P R}{R - r} = W$ .

$\frac{2 P R}{R - r} = W$

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.

$R - r, 1$

Remove parentheses.

$R - r, 1$

The LCM of one and any expression is the expression.

$R - r$

Multiply each term in $\frac{2 P R}{R - r} = W$ by $R - r$ to eliminate the fractions.

Multiply each term in $\frac{2 P R}{R - r} = W$ by $R - r$ .

$\frac{2 P R}{R - r} (R - r) = W (R - r)$

Simplify the left side.

Cancel the common factor of $R - r$ .

Cancel the common factor.

$\frac{2 P R}{R - r} (R - r) = W (R - r)$

Rewrite the expression.

$2 P R = W (R - r)$

Simplify the right side.

Apply the distributive property.

$2 P R = W R + W (- r)$

Rewrite using the commutative property of multiplication.

$2 P R = W R - W r$

Solve the equation.

Subtract $W R$ from both sides of the equation.

$2 P R - W R = - W r$

Factor $R$ out of $2 P R - W R$ .

Factor $R$ out of $2 P R$ .

$R (2 P) - W R = - W r$

Factor $R$ out of $- W R$ .

$R (2 P) + R (- W) = - W r$

Factor $R$ out of $R (2 P) + R (- W)$ .

$R (2 P - W) = - W r$

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

Divide each term in $R (2 P - W) = - W r$ by $2 P - W$ .

$\frac{R (2 P - W)}{2 P - W} = \frac{- W r}{2 P - W}$

Simplify the left side.

Cancel the common factor of $2 P - W$ .

Cancel the common factor.

$\frac{R (2 P - W)}{2 P - W} = \frac{- W r}{2 P - W}$

Divide $R$ by $1$ .

$R = \frac{- W r}{2 P - W}$

Simplify the right side.

Move the negative in front of the fraction.

$R = - \frac{W r}{2 P - W}$

Solve for R W=(2PR)/(R-r)

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