Solve for t Q=c/(1-t)

$Q = \frac{c}{1 - t}$

Step 1

Rewrite the equation as $\frac{c}{1 - t} = Q$ .

$\frac{c}{1 - t} = Q$

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.

$1 - t, 1$

Remove parentheses.

$1 - t, 1$

The LCM of one and any expression is the expression.

$1 - t$

Step 3

Multiply each term in $\frac{c}{1 - t} = Q$ by $1 - t$ to eliminate the fractions.

Multiply each term in $\frac{c}{1 - t} = Q$ by $1 - t$ .

$\frac{c}{1 - t} (1 - t) = Q (1 - t)$

Simplify the left side.

Cancel the common factor of $1 - t$ .

Cancel the common factor.

$\frac{c}{1 - t} (1 - t) = Q (1 - t)$

Rewrite the expression.

$c = Q (1 - t)$

Simplify the right side.

Apply the distributive property.

$c = Q \cdot 1 + Q (- t)$

Simplify the expression.

Multiply $Q$ by $1$ .

$c = Q + Q (- t)$

Rewrite using the commutative property of multiplication.

$c = Q - Q t$

Step 4

Solve the equation.

Rewrite the equation as $Q - Q t = c$ .

$Q - Q t = c$

Subtract $Q$ from both sides of the equation.

$- Q t = c - Q$

Divide each term in $- Q t = c - Q$ by $- 1 Q$ and simplify.

Divide each term in $- Q t = c - Q$ by $- 1 Q$ .

$\frac{- Q t}{- 1 Q} = \frac{c}{- 1 Q} + \frac{- Q}{- 1 Q}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{Q t}{Q} = \frac{c}{- 1 Q} + \frac{- Q}{- 1 Q}$

Cancel the common factor of $Q$ .

Cancel the common factor.

$\frac{Q t}{Q} = \frac{c}{- 1 Q} + \frac{- Q}{- 1 Q}$

Divide $t$ by $1$ .

$t = \frac{c}{- 1 Q} + \frac{- Q}{- 1 Q}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$t = - \frac{c}{Q} + \frac{- Q}{- 1 Q}$

Dividing two negative values results in a positive value.

$t = - \frac{c}{Q} + \frac{Q}{Q}$

Cancel the common factor of $Q$ .

Cancel the common factor.

$t = - \frac{c}{Q} + \frac{Q}{Q}$

Rewrite the expression.

$t = - \frac{c}{Q} + 1$

Solve for t Q=c/(1-t)

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