1Cademy - Solving $$\frac{D}{T} = R$$ for $$T$$

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Strategy to Solve Equations with Rational Expressions

Example

Solving $\frac{D}{T} = R$ for $T$

Solve the rational equation $\frac{D}{T} = R$ for the variable $T$ by applying the strategy for solving equations with rational expressions. This formula is the distance-rate-time relationship written in a form where the target variable $T$ appears in a denominator.

Step 1 — Identify restricted values. The variable $T$ appears in the denominator, so $T \neq 0$ .

Step 2 — Clear the fractions. The LCD is $T$ . Multiply both sides of the equation by $T$ :

$T \cdot \frac{D}{T} = T \cdot R$

Step 3 — Simplify. On the left, the $T$ in the numerator and denominator cancel:

$D = TR$

Step 4 — Isolate $T$ . Divide both sides by $R$ :

$\frac{D}{R} = T$

The solution is $T = \frac{D}{R}$ .

This example demonstrates that even a familiar formula like $D = RT$ becomes a rational equation when rewritten as $\frac{D}{T} = R$ , because the variable $T$ now appears in a denominator. The same clearing-fractions technique used for numerical rational equations — multiplying both sides by the LCD — is applied here to eliminate the denominator before isolating the target variable with a simple division.

Updated 2026-04-21

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OpenStax Elementary Algebra

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