Solve for f p=b-a/f

$p = b - \frac{a}{f}$

Step 1

Rewrite the equation as $b - \frac{a}{f} = p$ .

$b - \frac{a}{f} = p$

Step 2

Subtract $b$ from both sides of the equation.

$- \frac{a}{f} = p - b$

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.

$f, 1, 1$

The LCM of one and any expression is the expression.

$f$

Step 4

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

Multiply each term in $- \frac{a}{f} = p - b$ by $f$ .

$- \frac{a}{f} f = p f - b f$

Simplify the left side.

Cancel the common factor of $f$ .

Move the leading negative in $- \frac{a}{f}$ into the numerator.

$\frac{- a}{f} f = p f - b f$

Cancel the common factor.

$\frac{- a}{f} f = p f - b f$

Rewrite the expression.

$- a = p f - b f$

Step 5

Solve the equation.

Rewrite the equation as $p f - b f = - a$ .

$p f - b f = - a$

Factor $f$ out of $p f - b f$ .

Factor $f$ out of $p f$ .

$f p - b f = - a$

Factor $f$ out of $- b f$ .

$f p + f (- b) = - a$

Factor $f$ out of $f p + f (- b)$ .

$f (p - b) = - a$

Divide each term in $f (p - b) = - a$ by $p - b$ and simplify.

Divide each term in $f (p - b) = - a$ by $p - b$ .

$\frac{f (p - b)}{p - b} = \frac{- a}{p - b}$

Simplify the left side.

Cancel the common factor of $p - b$ .

Cancel the common factor.

$\frac{f (p - b)}{p - b} = \frac{- a}{p - b}$

Divide $f$ by $1$ .

$f = \frac{- a}{p - b}$

Simplify the right side.

Move the negative in front of the fraction.

$f = - \frac{a}{p - b}$

Solve for f p=b-a/f

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