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Stuck with a transposition, help??

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Toothpaste:
No problem, anytime.

Collin Li:

--- Quote from: "Timtasticle" ---(Image removed from quote.)


I always stuff these up. Can someone explain how to get the left hand side into the form of the right hand side?
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Faster way:

(2x+1) / (x-5) = [ 2(x-5) + 10 + 1 ] / (x-5) = 2 + 11/(x-5)

The trick is to force (x-5), the denominator to appear on the numerator, and create a compensation term (like you do with completing the square). I introduced 2(x-5) because we have 2x, so we need the 2 outside, then compensated by adding 10 (because 2*-5 from 2(x-5) would be -10). Added to the original 1, gives 11 as a remainder.

Feel free to ask for clarification, because I did rush that explanation.

kido_1:
Ah. Good old coblin.
Always to the rescue. :P

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