Solve for b 2=Q+f/b

$2 = Q + \frac{f}{b}$

Step 1

Rewrite the equation as $Q + \frac{f}{b} = 2$ .

$Q + \frac{f}{b} = 2$

Step 2

Subtract $Q$ from both sides of the equation.

$\frac{f}{b} = 2 - Q$

Step 3

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 4

Multiply each term in $\frac{f}{b} = 2 - Q$ by $b$ to eliminate the fractions.

Multiply each term in $\frac{f}{b} = 2 - Q$ by $b$ .

$\frac{f}{b} b = 2 b - Q b$

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{f}{b} b = 2 b - Q b$

Rewrite the expression.

$f = 2 b - Q b$

Step 5

Solve the equation.

Rewrite the equation as $2 b - Q b = f$ .

$2 b - Q b = f$

Factor $b$ out of $2 b - Q b$ .

Factor $b$ out of $2 b$ .

$b \cdot 2 - Q b = f$

Factor $b$ out of $- Q b$ .

$b \cdot 2 + b (- Q) = f$

Factor $b$ out of $b \cdot 2 + b (- Q)$ .

$b (2 - Q) = f$

Divide each term in $b (2 - Q) = f$ by $2 - Q$ and simplify.

Divide each term in $b (2 - Q) = f$ by $2 - Q$ .

$\frac{b (2 - Q)}{2 - Q} = \frac{f}{2 - Q}$

Simplify the left side.

Cancel the common factor of $2 - Q$ .

Cancel the common factor.

$\frac{b (2 - Q)}{2 - Q} = \frac{f}{2 - Q}$

Divide $b$ by $1$ .

$b = \frac{f}{2 - Q}$