## anonymous 5 years ago if I have an expression like this x/(x+1). I can divide numerator by denominator and get something like this 1-1/(x+1). Can someone teach me how to ...

1. anonymous

express the numerator as $\frac{ x+1-1}{x+1} = \frac{ x+1}{x+1} + \frac{-1}{x+1} = 1 \frac{1}{x+1}$

2. anonymous

$1- \frac{1}{x+1}$ that should be last part

3. anonymous

we add and subtract the same thing, so we dont change the value overall

4. anonymous

can you give me another example?

5. anonymous

take $\frac{x+2}{x+3}$

6. anonymous

so we look on the bottom , it has x+3 , so we want to see an x+3 in the numerator

7. anonymous

so express as $\frac{x+3+2 -3 }{x+3} = \frac{x+3 -1 }{x+3}$

8. anonymous

$= \frac{x+3}{x+3} - \frac{1}{x+3} = 1 - \frac{1}{x+3}$

9. anonymous

its all fairly standard

10. anonymous

so you mean I have to look at the bottom. if I have for example (x+4), then I have to add and substract 4 and -4 respectively?

11. anonymous

yes , all it relys on is being able to split up the numerators

12. anonymous

in the numerator

13. anonymous

ok im gonna give you an example. Please check if it is correct

14. anonymous

$x/(1+x^{2})$well i dont know what to do here :(

15. anonymous

thats why it only works with linear terms in the numerator and denominator

16. anonymous

you cant break that up

17. anonymous

partial fractions? idk you need a constant on top

18. anonymous

but that cant be broken down

19. anonymous

ya

20. anonymous

you cant just make up random examples

21. anonymous

or you could have something like $\frac{x^2 +2x} {(x+1)^2}$

22. anonymous

So how should I do in cases like this. that is why I dont understand The oiginal problems starts there

23. anonymous

the question is badly written, I would just ignore it, it cant be broken down further , teacher is stupid

24. anonymous

Sorry dude but im working with integrals. They have an expression like that and get that answer. the answer is 1-1(x2 +1)

25. anonymous

I dont understand whart u mean

26. anonymous

but if you want $\int\limits \frac{x}{1+x^2} dx$

27. anonymous

then its a logarithm

28. anonymous

yeah that is right

29. anonymous

in a book im reading, they say that $x ^{2}/(1+x ^{2})=1-1/(1+x ^{2})$

30. anonymous

$= \frac{1}{2} \ln ( 1+x^2) +$

31. anonymous

my question is how do I do that

32. anonymous

ohh yeh, now you have changed the question :|

33. anonymous

sorry lol

34. anonymous

add and subtract 1 on the top and bottom

35. anonymous

$=\frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1- \frac{1}{x^2+1}$

36. anonymous

very basic, nothing really hard

37. anonymous

nice

38. anonymous

ok cool. sorry for me to make you feel angry lol