Solve for t p=a/(1+rt)

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

Step 1

Rewrite the equation as $\frac{a}{1 + r t} = p$ .

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

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.

$1 + r t, 1$

Remove parentheses.

$1 + r t, 1$

The LCM of one and any expression is the expression.

$1 + r t$

Step 3

Multiply each term in $\frac{a}{1 + r t} = p$ by $1 + r t$ to eliminate the fractions.

Multiply each term in $\frac{a}{1 + r t} = p$ by $1 + r t$ .

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

Simplify the left side.

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

Cancel the common factor.

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

Rewrite the expression.

$a = p (1 + r t)$

Simplify the right side.

Apply the distributive property.

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

Multiply $p$ by $1$ .

$a = p + p r t$

Step 4

Solve the equation.

Rewrite the equation as $p + p r t = a$ .

$p + p r t = a$

Subtract $p$ from both sides of the equation.

$p r t = a - p$

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

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

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

Simplify the left side.

Cancel the common factor of $p$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $r$ .

Cancel the common factor.

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

Divide $t$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $p$ .

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Solve for t p=a/(1+rt)

Related Questions

Support LCMGCF.com by disabling your adblocker.