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# Proper fraction watch

1. How do I go about putting

(x^2+2x)/(x+1) Into a proper fraction. My mind is just blank right now. I have tried long division and trying to factorise the numerator but it hasn't helped me see how to do it

Thank you!!
2. (Original post by HaNzY)
How do I go about putting

(x^2+2x)/(x+1) Into a proper fraction. My mind is just blank right now. I have tried long division and trying to factorise the numerator but it hasn't helped me see how to do it

Thank you!!
Here is a start.

3. (Original post by steve2005)
Here is a start.

Okay so I have x + (x/(x+1)) now I have to integrate it between 2 and 1
and I get-

[ x^2/2 + x ln |x+1| ]

= 2 + 2ln3 - (1/2 + ln2)

= 1.5 + 2ln(3/2)

Yet the answer book says 2.5 + ln(2/3)

So I am not sure where I have gone wrong at all, is there something blindingly obvious that I have done wrong?
4. (Original post by HaNzY)
Okay so I have x + (x/(x+1)) now I have to integrate it between 2 and 1
and I get-

[ x^2/2 + x ln |x+1| ]

= 2 + 2ln3 - (1/2 + ln2)

= 1.5 + 2ln(3/2)

Yet the answer book says 2.5 + ln(2/3)

So I am not sure where I have gone wrong at all, is there something blindingly obvious that I have done wrong?

Long division will work; perhaps you made a slip in the algebra.

x/(1+x) is still an improper fraction.

The integral of x/(1+x) is not x ln |x+1|
5. (Original post by ghostwalker)

Long division will work; perhaps you made a slip in the algebra.

x/(1+x) is still an improper fraction.

The integral of x/(1+x) is not x ln |x+1|
Oh, this is annoying, what is the proper fraction of the question I am doing then?? and for the integral, the book says-

integral of 1/ax+b dx = 1/a ln |ax+b| + c

and as far I am aware with this formula the integral of x/(x+1) is x ln |x+1|

????? I'm confused
6. (Original post by HaNzY)
Oh, this is annoying, what is the proper fraction of the question I am doing then??
To get it as a proper fraction, you need to get the the degree (the highest power that x is raised to) of the numerator to be less than that of the denominator. With ...+ x/(x+1), they are both 1. So you need to take the division one step further to get .... + 1 - 1/(x+1)

and for the integral, the book says-

integral of 1/ax+b dx = 1/a ln |ax+b| + c

and as far I am aware with this formula the integral of x/(x+1) is x ln |x+1|
Whilst what the book says is true, what you are "aware of" does not follow. You can only say that a/(x+1) integrates to a ln |x+1| where "a" is a constant. It doesn't work if you have a function of x in the numerator. I don't know what you've covered, so don't want to comment further on that aspect.
7. (Original post by ghostwalker)
To get it as a proper fraction, you need to get the the degree (the highest power that x is raised to) of the numerator to be less than that of the denominator. With ...+ x/(x+1), they are both 1. So you need to take the division one step further to get .... + 1 - 1/(x+1)

Whilst what the book says is true, what you are "aware of" does not follow. You can only say that a/(x+1) integrates to a ln |x+1| where "a" is a constant. It doesn't work if you have a function of x in the numerator. I don't know what you've covered, so don't want to comment further on that aspect.

Ooooooooo it has just clicked! x/x+1 can be made into 1 - 1/x+1 !!! It always ends up being that I miss the complete obvious things. I really need to remember I can add numbers as long as I minus them again. Grrr. Thank you very much. Yeah I thought it may not be correct if it was x in the numerator. Oooo it works and I have the correct answer now! Thank you
8. If you are trying to integrate (x^2 + 2x)/(x+1) you can use the fact x^2 + 2x = (x+1)^2 - 1 to write it as x+1 - 1/(x+1). This makes the integration simpler.
9. (Original post by HaNzY)
How do I go about putting

(x^2+2x)/(x+1) Into a proper fraction. My mind is just blank right now. I have tried long division and trying to factorise the numerator but it hasn't helped me see how to do it

Thank you!!

is this c3 or c4?? if it's c4 use cover-up method. I haven't done C4 yet, but i've had a peek and it looks interesting.
10. (Original post by Remarqable M)
is this c3 or c4?? if it's c4 use cover-up method. I haven't done C4 yet, but i've had a peek and it looks interesting.
Yeah it's C4, the thing is I am resitting it because my mark on it made me get one UMS mark away from an A overall!! And so I haven't done maths since June and I really feel like an idiot as if I am brand new to it lol! I will have a look at the cover up method because I really need to get a method in my head that I know will work in the exam!!
11. (Original post by Drederick Tatum)
If you are trying to integrate (x^2 + 2x)/(x+1) you can use the fact x^2 + 2x = (x+1)^2 - 1 to write it as x+1 - 1/(x+1). This makes the integration simpler.
I can see that now, but how do you spot things like this quickly in the exam?? That is where I fall down, simple stuff that I am blind to! I can do the hard stuff and remembering formulas and whatever, it's just I suck at manipulating things like this lol!

I can't even look at a quadratic and straight away put it in brackets when factorising, I have to use a method that my GCSE teacher taught me! (It's not too long winded, but the point is, I have no idea how to go straight to brackets lol!) Simple things are the hardest for me blllaaaahhh LOL. Thank you for all your help guys

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