Talk:High School Mathematics Extensions/Supplementary/Partial Fractions

Repeated Factors?
Should the discussion include what happens when there is a repeated factor in the denominator, like
 * $$\frac{4x-1}{(x+2)^2 (x-1)}$$? --Jwwalker 04:35, 15 Mar 2005 (UTC)


 * I'm now writing this part, thank you for bringing it into attention. --Lemontea 12:59, 15 Mar 2005 (UTC)

Divison by zero
'2. General method' proposes an exercise do determine p, such that (3p - 21) / ((p - 5)p - 14) is equal to 1 / 3

I've solved the exercise with methods that I knew and the method being taught to me finding 7 as the possible solution

however, p = 7 results 0 / 0 = 1 / 3 for the initial equation, which is a paradoxical equation

I've assumed this was a typo, in wich we're supossed to solve (3p - 21) / ((p - 5)(p - 14)) = 1 / 3, however this leads to p² - 28p + 133 = 0, which does not have whole solutions

I suppose this exercise is meant to have whole solutions. So i've found an similar equation to be solved:

(3p - 21) / ((p - 19)p + 84) = 1 / 3

writing the first part as a sum of fractions results in 0 / (p - 7) + 3 / (p - 12) = 1 / 3, which I believe is a necessary step for the exercise. This results in p = 21, which does not create a paradox for the original equation

the other path that leads to to p² - 28p + 147 = 0 also lists p = 7 as a possible solution, however this is not valid as it also leads to 0 / 0 = 1 / 3 Slidey-0766 (discuss • contribs) 17:52, 9 February 2024 (UTC)