Solve for F R=F/(N+F)

$R = \frac{F}{N + F}$

Step 1

Rewrite the equation as $\frac{F}{N + F} = R$ .

$\frac{F}{N + F} = R$

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.

$N + F, 1$

Remove parentheses.

$N + F, 1$

The LCM of one and any expression is the expression.

$N + F$

Step 3

Multiply each term in $\frac{F}{N + F} = R$ by $N + F$ to eliminate the fractions.

Multiply each term in $\frac{F}{N + F} = R$ by $N + F$ .

$\frac{F}{N + F} (N + F) = R (N + F)$

Simplify the left side.

Cancel the common factor of $N + F$ .

Cancel the common factor.

$\frac{F}{N + F} (N + F) = R (N + F)$

Rewrite the expression.

$F = R (N + F)$

Simplify the right side.

Apply the distributive property.

$F = R N + R F$

Step 4

Solve the equation.

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

$F - R F = R N$

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

Factor $F$ out of $F^{1}$ .

$F \cdot 1 - R F = R N$

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

$F \cdot 1 + F (- R) = R N$

Factor $F$ out of $F \cdot 1 + F (- R)$ .

$F (1 - R) = R N$

Divide each term in $F (1 - R) = R N$ by $1 - R$ and simplify.

Divide each term in $F (1 - R) = R N$ by $1 - R$ .

$\frac{F (1 - R)}{1 - R} = \frac{R N}{1 - R}$

Simplify the left side.

Cancel the common factor of $1 - R$ .

Cancel the common factor.

$\frac{F (1 - R)}{1 - R} = \frac{R N}{1 - R}$

Divide $F$ by $1$ .

$F = \frac{R N}{1 - R}$