College Algebra / Unit 2 Alg 117 worked example, 60 to 90 seconds
Simplifying a Complex Rational Expression
The idea
A complex rational expression carries rational expressions inside its numerator or denominator; simplifying means collapsing each floor to a single fraction, then dividing.
In practice
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.
Where people slip
Collapse before dividing; flipping a still-summed floor is the denominator-split error in disguise.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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