PARTIAL FRACTIONS: RULE 1
PAGE 1 OF 5, THE REVERSE OF ADDING FRACTIONS
SPLIT IT UP
PULL A COMPLEX FRACTION APART
You have spent years learning to add fractions: find a common denominator, combine numerators, simplify. Partial fractions run the movie backwards. Start with one rational expression whose denominator is a product of simpler factors, and rewrite it as a sum of simpler fractions. Why bother? Because a sum like A/(x − a) + B/(x − b) is far easier to integrate, differentiate, or solve in equations than one big fraction with a multiplied denominator. Rule 1 covers the cleanest case: distinct linear factors in the bottom, nothing repeated, nothing quadratic yet.
⚡ BIG IDEA
Partial fractions turn "one awkward fraction" into "several easy ones." It is the reverse of adding over a common denominator.
SPLIT!
ONE FRACTION
📜 One complicated top/bottom
🔗 Denominator factorised
🎯 Target for splitting
🔗 Denominator factorised
🎯 Target for splitting
SUM OF PARTS
➕ Several easy pieces
🔢 Unknown constants A, B…
✅ Same value overall
🔢 Unknown constants A, B…
✅ Same value overall