Solve for d (ab)/d+c=e

$\frac{a b}{d} + c = e$

Step 1

Subtract $c$ from both sides of the equation.

$\frac{a b}{d} = e - c$

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.

$d, 1, 1$

The LCM of one and any expression is the expression.

$d$

Step 3

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

Multiply each term in $\frac{a b}{d} = e - c$ by $d$ .

$\frac{a b}{d} d = e d - c d$

Simplify the left side.

Cancel the common factor of $d$ .

Cancel the common factor.

$\frac{a b}{d} d = e d - c d$

Rewrite the expression.

$a b = e d - c d$

Step 4

Solve the equation.

Rewrite the equation as $e d - c d = a b$ .

$e d - c d = a b$

Factor $d$ out of $e d - c d$ .

Factor $d$ out of $e d$ .

$d e - c d = a b$

Factor $d$ out of $- c d$ .

$d e + d (- c) = a b$

Factor $d$ out of $d e + d (- c)$ .

$d (e - c) = a b$

Divide each term in $d (e - c) = a b$ by $e - c$ and simplify.

Divide each term in $d (e - c) = a b$ by $e - c$ .

$\frac{d (e - c)}{e - c} = \frac{a b}{e - c}$

Simplify the left side.

Cancel the common factor of $e - c$ .

Cancel the common factor.

$\frac{d (e - c)}{e - c} = \frac{a b}{e - c}$

Divide $d$ by $1$ .

$d = \frac{a b}{e - c}$