Solve for p t=(a-p)/(pr)

$t = \frac{a - p}{p r}$

Step 1

Rewrite the equation as $\frac{a - p}{p r} = t$ .

$\frac{a - p}{p r} = t$

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.

$p r, 1$

The LCM of one and any expression is the expression.

$p r$

Step 3

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

Multiply each term in $\frac{a - p}{p r} = t$ by $p r$ .

$\frac{a - p}{p r} (p r) = t (p r)$

Simplify the left side.

Cancel the common factor of $p r$ .

Cancel the common factor.

$\frac{a - p}{p r} (p r) = t (p r)$

Rewrite the expression.

$a - p = t (p r)$

Simplify the right side.

Remove parentheses.

$a - p = t p r$

Step 4

Solve the equation.

Subtract $t p r$ from both sides of the equation.

$a - p - t p r = 0$

Subtract $a$ from both sides of the equation.

$- p - t p r = - a$

Factor $p$ out of $- p - t p r$ .

Factor $p$ out of $- p$ .

$p \cdot - 1 - t p r = - a$

Factor $p$ out of $- t p r$ .

$p \cdot - 1 + p (- t r) = - a$

Factor $p$ out of $p \cdot - 1 + p (- t r)$ .

$p (- 1 - t r) = - a$

Divide each term in $p (- 1 - t r) = - a$ by $- 1 - t r$ and simplify.

Divide each term in $p (- 1 - t r) = - a$ by $- 1 - t r$ .

$\frac{p (- 1 - t r)}{- 1 - t r} = \frac{- a}{- 1 - t r}$

Simplify the left side.

Cancel the common factor of $- 1 - t r$ .

Cancel the common factor.

$\frac{p (- 1 - t r)}{- 1 - t r} = \frac{- a}{- 1 - t r}$

Divide $p$ by $1$ .

$p = \frac{- a}{- 1 - t r}$

Simplify the right side.

Move the negative in front of the fraction.

$p = - \frac{a}{- 1 - t r}$

Rewrite $- 1$ as $- 1 (1)$ .

$p = - \frac{a}{- 1 (1) - t r}$

Factor $- 1$ out of $- t r$ .

$p = - \frac{a}{- 1 (1) - (t r)}$

Factor $- 1$ out of $- 1 (1) - (t r)$ .

$p = - \frac{a}{- 1 (1 + t r)}$

Simplify the expression.

Move the negative in front of the fraction.

$p = - - \frac{a}{1 + t r}$

Multiply $- 1$ by $- 1$ .

$p = 1 \frac{a}{1 + t r}$

Multiply $\frac{a}{1 + t r}$ by $1$ .

$p = \frac{a}{1 + t r}$

Solve for p t=(a-p)/(pr)

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