# Thread: Finding the standard form of a rational function

1. ## Finding the standard form of a rational function

Find the standard form for (20x^2+11x-1)/(4x+3)?

Not sure what 'standard' form means, help would be appreciated

2. I'm not sure what is meant either, but maybe the requirement is to perform polynomial long division here?

I.e make $\displaystyle \displaystyle \frac{20x^2+11x-1}{4x+3} = a+\frac{b}{4x+3}$

3. well after finding the standard form, I'm asked to find all straight line asymptotes (vertical, horizontal or oblique), maybe that might give a clue?

4. Well now knowing this, my advice in post #2 is the way forward.

5. How do I find a and b? Would you be able to show me an example (I've got quite a few of these to do and seeing the steps would help a lot!)

6. Polynomial long division is the road I would take.

Follow this example

Polynomial Long Division

Spoiler:
$\displaystyle \displaystyle \frac{20x^2+11x-1}{4x+3} = 5x-1+\frac{2}{4x+3}$

7. Thanks a lot, I really appreciate it

8. Are you aware of what this means in context of the following question about asymptotes?

9. I just did all the working out for the question using the example, thanks a lot! For the asymptotes, I'm not sure how to figure them out in this form. Don't I have to find where (4x+3) is 0 so that it is infinity or something along those lines?

Is the slant/oblique asymptote just 5x-1? and I think there is no vertical or horizontal asymptotes

10. Originally Posted by brumby_3
Don't I have to find where (4x+3) is 0
Yep, solve 4x+3=0, that is the vertical asymptote.

Originally Posted by brumby_3

Is the slant/oblique asymptote just 5x-1?
Yep!

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### rational function general form to standard form

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