Solve for b x=(ab+c)/b-d

$x = \frac{a b + c}{b} - d$

Step 1

Rewrite the equation as $\frac{a b + c}{b} - d = x$ .

$\frac{a b + c}{b} - d = x$

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.

$b, 1, 1$

The LCM of one and any expression is the expression.

$b$

Step 3

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

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

$\frac{a b + c}{b} b - d b = x b$

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{a b + c}{b} b - d b = x b$

Rewrite the expression.

$a b + c - d b = x b$

Step 4

Solve the equation.

Subtract $x b$ from both sides of the equation.

$a b + c - d b - x b = 0$

Subtract $c$ from both sides of the equation.

$a b - d b - x b = - c$

Factor $b$ out of $a b - d b - x b$ .

Factor $b$ out of $a b$ .

$b a - d b - x b = - c$

Factor $b$ out of $- d b$ .

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

Factor $b$ out of $- x b$ .

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

Factor $b$ out of $b a + b (- d)$ .

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

Factor $b$ out of $b (a - d) + b (- x)$ .

$b (a - d - x) = - c$

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

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

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

Simplify the left side.

Cancel the common factor of $a - d - x$ .

Cancel the common factor.

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

Divide $b$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Solve for b x=(ab+c)/b-d

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