Rational equations

A rational equation has the variable in a denominator. Multiply through by the denominator (x ≠ 0), solve, and check the answer does not make any denominator zero.

12/x = 4Rational equations

📐 Formula

a/x = b ⇒ x = a/b (x ≠ 0)

✏️ Worked example

12/x = 4 ⇒ 12 = 4x ⇒ x = 3. The curve y = 12/x meets the line y = 4 at x = 3.

🌍 Where it is used

Work and rate problems: time = work ÷ rate.

❓ Quick check

Solve 10/x = 2.

🏋️ Practice

Easy6/x = 3

Answer: x = 2

Medium(x + 1)/x = 3

Answer: x = ½

ChallengeOne pipe fills a tank in 6 h, another in 3 h. Together?

Answer: 2 hours