Simplifying a Complex Rational Expression

A complex rational expression carries rational expressions inside its numerator or denominator; simplifying means collapsing each floor to a single fraction, then dividing.

Simplify (1/x + 1/2) ÷ (1/x) — a fraction built of fractions. First collapse the top: 1/x + 1/2 over the LCD 2x is (2 + x)/(2x). The bottom is already a single fraction. Now divide: (2 + x)/(2x) · x/1 = (2 + x)/2. Spot-check at x = 2: the top is 1/2 + 1/2 = 1, the bottom is 1/2, and 1 ÷ 1/2 = 2; the simplified form gives (2 + 2)/2 = 2. One collapse, one flip, one cancel — and the spot-check seals it. The same three moves clear any stack of floors.