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Recently I had taken the SATs, and a question came up that involved partial fractions decomposition.

$$\frac{x^2-4x+5}{x-3}$$

This is not the exact problem but a similar one. If the SAT math is supposed to go up to Algebra 2, in what class are partial fractions taught?

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closed as unclear what you're asking by András Bátkai, Henry Towsner, celeriko, Benjamin Dickman, JoeTaxpayer Oct 9 '16 at 18:54

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    $\begingroup$ I don't understand; this is just a fraction. What's the actual problem? $\endgroup$ – Henry Towsner Oct 4 '16 at 1:32
  • $\begingroup$ @HenryTowsner I was wondering in what level of math are partial fractions thought, is really my only question. $\endgroup$ – EnlightenedFunky Oct 4 '16 at 1:33
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    $\begingroup$ If you're going to illustrate the question with an example problem, the problem should be stated coherently. Alternatively, you could drop the entire discussion about the SAT if it's not actually relevant to the question. $\endgroup$ – Henry Towsner Oct 4 '16 at 1:37
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    $\begingroup$ @EnlightenedFunky: To be clarify what I think Henry is asking, a proper mathematical exercise requires a natural-language direction. For example, including "Write the partial fraction decomposition of... " or "Divide the polynomials" in your quoted part would be satisfactory. $\endgroup$ – Daniel R. Collins Oct 5 '16 at 0:31
  • $\begingroup$ @DanielR.Collins: Yes, exactly. I'm still very confused by this whole question, because if the question is "what level of math are partial fractions taught in", I don't understand why an answer which doesn't address that in any way has been accepted. $\endgroup$ – Henry Towsner Oct 5 '16 at 16:36
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Sure this isn't a typo, or maybe for the SAT math subject test (once known as SAT II?) I would be surprised if partial fractions were part of this ... on the other hand, synthetic division of polynomials is quite likely, but then the answer here would be $$(x-1)+\frac{2}{x-3}$$ But usually that's not what we think of as "partial fractions".

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  • $\begingroup$ I think you are right, I probably just over thought the question. $\endgroup$ – EnlightenedFunky Oct 4 '16 at 1:02
  • $\begingroup$ But couldn't the question be solved using partial fractions too? Yes I got that same answer you achieved. $\endgroup$ – EnlightenedFunky Oct 4 '16 at 1:03
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    $\begingroup$ Well, partial fractions typical is only thought of when one is looking at a denominator that itself can be factored. Otherwise it really reduces to long division. I do think your question has merit if one asks when is such division taught and is it appropriate for SAT. $\endgroup$ – kcrisman Oct 4 '16 at 1:43
  • $\begingroup$ +1 Perfect couldn't have said it better myself. $\endgroup$ – EnlightenedFunky Oct 4 '16 at 3:04

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