7.10 Partial Fraction Decomposition

We won’t be using this technique until Question 15.4.10, so feel free to skip this section, although it would be good practice for many of the skills you’ve learned so far.

We know from Question 7.4.19 that we can rewrite \[\frac{a}{b} + \frac{c}{d}\] as \[\frac{ad + cb}{bd}.\]

Question 7.10.1

Sometimes we want to do the reverse of that. Rewrite \[\frac{2x+1}{(x+3)(2x-1)}\] in the form \[\frac{A}{x+3} + \frac{B}{2x-1}\] where $A$ and $B$ are real numbers. The reason we might want to do this is that the second expression is easier to integrate (Section 15.4: Integration) than the first. Show hint

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Question 7.10.2

Rewrite \[\frac{7x-13}{x^2 - 5x + 4}\] in the form \[\frac{A}{Cx+D} + \frac{B}{Ex+F}.\] Show hint

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