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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Timtasticle on November 10, 2007, 04:18:32 pm

Title: Stuck with a transposition, help??
Post by: Timtasticle on November 10, 2007, 04:18:32 pm

(http://img246.imageshack.us/img246/6778/imaspudxq0.jpg)


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

Title: Stuck with a transposition, help??
Post by: Toothpaste on November 10, 2007, 04:32:25 pm

Long division. :D

Title: Stuck with a transposition, help??
Post by: Timtasticle on November 10, 2007, 04:36:06 pm

I see, care to elaborate?

Title: Stuck with a transposition, help??
Post by: Toothpaste on November 10, 2007, 04:38:23 pm

(http://i148.photobucket.com/albums/s4/Toothpick00/longdiv.gif)


hence:

(2x+1)/(x-5)

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

hope that made sense.

"answer" plus [ "remainder" / "what you are dividing it by(denominator)" ]

Title: Stuck with a transposition, help??
Post by: Timtasticle on November 10, 2007, 04:39:55 pm

Oooohh I see. :o

I always try and separate the fractions  :oops:

Thanks heaps for your help!!

Title: Stuck with a transposition, help??
Post by: Toothpaste on November 10, 2007, 04:44:21 pm

No problem, anytime.

Title: Re: Stuck with a transposition, help??
Post by: Collin Li on November 10, 2007, 05:11:07 pm

Quote from: "Timtasticle"

(http://img246.imageshack.us/img246/6778/imaspudxq0.jpg)


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

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.

Title: Stuck with a transposition, help??
Post by: kido_1 on November 10, 2007, 05:50:12 pm

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