M5.1.5 For the adult
Partial fractions
Can I split (3x + 5)/((x + 1)(x + 2)) into fractions with one bracket each on the bottom?
What this chapter teaches
Partial fractions split one fraction with a product on the bottom into plainer fractions, one for each bracket. A repeated bracket (x + 1)² needs two parts: one over (x + 1) and one over (x + 1)². The letters are found by equating coefficients, or by the cover up shortcut. A top that is not lower in degree than the bottom is divided first.
Three questions to ask
There is no one right wording. Listen for the idea.
- What form would you write for 5/((x − 1)(x + 3))?
- Why does a squared bracket on the bottom need two parts?
- How can you check a split using one number for x?
After the chapter, the learner can
- Split (3x + 5)/((x + 1)(x + 2)) into two simpler fractions
- Split a fraction with a repeated factor on the bottom
What they copy into their notebook
One part for each bracket. A squared bracket needs A/(x + a) + B/(x + a)². Find letters by equating coefficients; the cover up checks. Divide first if the top is not lower.