HALP

since math is the department where i fail most, i need help with my homework.
my brain totally froze and i can't work this, even though i know that it's easy and i should know it. but i just don't.

f(x)= x²/x²-4
should explain how f(x) can also be written under this form: f(x)= 1 + a/(x-2) + b/(x+2)
where a and b are two real numbers to determine.

i tried doing it like this
x²/x²-4 = 1 + a/(x-2) + b/(x+2)
and you know do it by comparision, but that's wrong because i'd get (a+b)=0 and i should at least at this point know a so i know b.

help, please?

after writing that, send 1 to the other side. it should be like this.


x²/x²-4 - (1)=a/(x-2) + b/(x+2)

organize this and it becomes this

4/x²-4=a/(x-2) + b/(x+2) (x²s go.)

and i think you can do other steps.

final result is a=1 and b= -1.

you can ask me again if you have a problem.

thank you so much for the help! : ) <3

okay i did it and got
4/x²-4 = a+b/x²-4

did i do it wrong? :s

what i actually did is moved the 1 to the other side like you said
x²/x²-4 (-1) = a/(x-2) + b/(x+2)
x²-(x²-4)/x²-4 = a+b/ x²-4
x²-x²+4/x²-4 = a+b/x²-4
4/x²-4 = a+b/x²-4

that's the only way i thought of when i had to know a and b but it doesn't work ?


also i should mention that this exercise is in the logarithm chapter, so idk if it got anything to do with logarithm? though i'm sure we didn't learn anything to do with finding unknown numbers through logarithm or integrals.

4/x²-4=a/(x-2)+b/(x+2) you are correct but you forgot to write something so it looks wrong.

after this step it becomes like that

4/x²-4=a(x+2)+b(x-2)/x²-4 then we don't care "x²-4" because both sides are equal.

4=a(x+2)+b(x-2) to find a and b easily i organized it.

4=ax+2a+bx-2b

4=x(a+b)+2(a-b) see that there's no "x" on the other side so that means a+b=0, 4=2(a-b)

a+b=0
a-b=2

when you solve these 2 things together a=1 and b=-1

hmm i dont remember using this in logarithm but we used it in integrals to take it out of the integral.( hope you get what i mean)

(the big S which means integral) x²/x²-4 when it's like that you can't find the deriative of this function so it must be simplized using what we did in your question.


(the big S which means integral) 1+1/(x-2)-1(x+2)=(the big S which means integral) x²/x²-4

i hope you understand what i'm trying to explain. i studied all of these in high school in turkish, now studying them in again in english but it's really hard to explain it on the internet.

ahhh thank you!
see, i did all this that you mentioned:
4/x²-4=a/(x-2)+b/(x+2) you are correct but you forgot to write something so it looks wrong.

after this step it becomes like that

4/x²-4=a(x+2)+b(x-2)/x²-4 then we don't care "x²-4" because both sides are equal.

4=a(x+2)+b(x-2) to find a and b easily i organized it.

4=ax+2a+bx-2b

4=x(a+b)+2(a-b) see that there's no "x" on the other side so that means a+b=0, 4=2(a-b)
----

but i didn't think of solving the two of them together like this
a+b=0
a-b=2
...
thank you.

and i totally understand what you mean! i study them in french so it was also hard to explain what i meant in the first place, but i get your explanation. (:

and i don't understand math easily, so you definitely scored there hahaa.

btw, thanks for the integral explanation it helped me do the following question.

oh i'm happy that it helped you.

well math was really hard for me but now it's really easy and i dont know how it had happened.

you were a great help.
well i bet your life is a bit easier now.

are you in college now?

Aaah yeeps if you say college instead of uni yeps

cool. xD yeah i meant uni.

what are you studying? if you don't mind me asking lol

Business Administration. aha you're still in high school ?

yeah. -_- last year hopefully.

hope you'll get into the college you want.

thanks hun, i can't wait.
is that your first year in uni?

yeeps. it's really different than high school looools