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**torx****Member**- Registered: 2006-03-25
- Posts: 4

My tutor was showing me some steps to solve a Curve Sketching problem and i am unable to understand a part of it.

Specifically, i don't understand how my tutor was able to go from:

y= (x^2 + 2x + 2) / (x+3)(x-1)

To:

y= 1 + (5) / ((x+3)(x-1))

He did mention something about the first expression being an Improper Fraction and has to be divided.

So if anyone know how to go from the first to the second expression, please help. Thanks!

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,945

An improper fraction is a fraction where the numerator is greater than the denominator (like 7/5 which can be expressed as a proper fraction as 1 2/5). An improper fraction can be converted into a proper fraction by dividing the numerator by the denominator.

In this case, the numerator is x²+2x+2 and the denominator is x²+2x-3 (Multiplying the two terms in the denominator(x+3) and (x-1)) .

When the numerator is divided by the denominator, quotient 1 is obtained and the reminder is 5.

Therefore, the expression can be written as 1 + 5/[(x+3)(x-1)].

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**torx****Member**- Registered: 2006-03-25
- Posts: 4

okay. but i'm not really sure how to go about doing the division. I tried factorising it and cancelling out but it doesn't work. searching on the net doesnt yield anything useful too.

so it would be really helpful if you could elaborate on the steps for doing the divison or direct me to a site.

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**torx****Member**- Registered: 2006-03-25
- Posts: 4

bump

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**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 121

Check out **http://www.sosmath.com/algebra/factor/fac01/fac01.html** it explains what you need to know.

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**torx****Member**- Registered: 2006-03-25
- Posts: 4

Exactly what i'm looking for!

That really helped! Thanks!

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