Solve for d f=d/(e-d)

$f = \frac{d}{e - d}$

Step 1

Rewrite the equation as $\frac{d}{e - d} = f$ .

$\frac{d}{e - d} = f$

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.

$e - d, 1$

Remove parentheses.

$e - d, 1$

The LCM of one and any expression is the expression.

$e - d$

Step 3

Multiply each term in $\frac{d}{e - d} = f$ by $e - d$ to eliminate the fractions.

Multiply each term in $\frac{d}{e - d} = f$ by $e - d$ .

$\frac{d}{e - d} (e - d) = f (e - d)$

Simplify the left side.

Cancel the common factor of $e - d$ .

Cancel the common factor.

$\frac{d}{e - d} (e - d) = f (e - d)$

Rewrite the expression.

$d = f (e - d)$

Simplify the right side.

Apply the distributive property.

$d = f e + f (- d)$

Rewrite using the commutative property of multiplication.

$d = f e - f d$

Step 4

Solve the equation.

Add $f d$ to both sides of the equation.

$d + f d = f e$

Factor $d$ out of $d + f d$ .

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

$d \cdot 1 + f d = f e$

Factor $d$ out of $f d$ .

$d \cdot 1 + d f = f e$

Factor $d$ out of $d \cdot 1 + d f$ .

$d (1 + f) = f e$

Divide each term in $d (1 + f) = f e$ by $1 + f$ and simplify.

Divide each term in $d (1 + f) = f e$ by $1 + f$ .

$\frac{d (1 + f)}{1 + f} = \frac{f e}{1 + f}$

Simplify the left side.

Cancel the common factor of $1 + f$ .

Cancel the common factor.

$\frac{d (1 + f)}{1 + f} = \frac{f e}{1 + f}$

Divide $d$ by $1$ .

$d = \frac{f e}{1 + f}$

Solve for d f=d/(e-d)

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