anonymous
  • anonymous
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 ...
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
express the numerator as \[\frac{ x+1-1}{x+1} = \frac{ x+1}{x+1} + \frac{-1}{x+1} = 1 \frac{1}{x+1} \]
anonymous
  • anonymous
\[1- \frac{1}{x+1}\] that should be last part
anonymous
  • anonymous
we add and subtract the same thing, so we dont change the value overall

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anonymous
  • anonymous
can you give me another example?
anonymous
  • anonymous
take \[\frac{x+2}{x+3} \]
anonymous
  • anonymous
so we look on the bottom , it has x+3 , so we want to see an x+3 in the numerator
anonymous
  • anonymous
so express as \[\frac{x+3+2 -3 }{x+3} = \frac{x+3 -1 }{x+3}\]
anonymous
  • anonymous
\[= \frac{x+3}{x+3} - \frac{1}{x+3} = 1 - \frac{1}{x+3}\]
anonymous
  • anonymous
its all fairly standard
anonymous
  • 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?
anonymous
  • anonymous
yes , all it relys on is being able to split up the numerators
anonymous
  • anonymous
in the numerator
anonymous
  • anonymous
ok im gonna give you an example. Please check if it is correct
anonymous
  • anonymous
\[x/(1+x^{2})\]well i dont know what to do here :(
anonymous
  • anonymous
thats why it only works with linear terms in the numerator and denominator
anonymous
  • anonymous
you cant break that up
anonymous
  • anonymous
partial fractions? idk you need a constant on top
anonymous
  • anonymous
but that cant be broken down
anonymous
  • anonymous
ya
anonymous
  • anonymous
you cant just make up random examples
anonymous
  • anonymous
or you could have something like \[\frac{x^2 +2x} {(x+1)^2} \]
anonymous
  • anonymous
So how should I do in cases like this. that is why I dont understand The oiginal problems starts there
anonymous
  • anonymous
the question is badly written, I would just ignore it, it cant be broken down further , teacher is stupid
anonymous
  • 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)
anonymous
  • anonymous
I dont understand whart u mean
anonymous
  • anonymous
but if you want \[\int\limits \frac{x}{1+x^2} dx \]
anonymous
  • anonymous
then its a logarithm
anonymous
  • anonymous
yeah that is right
anonymous
  • anonymous
in a book im reading, they say that \[x ^{2}/(1+x ^{2})=1-1/(1+x ^{2})\]
anonymous
  • anonymous
\[= \frac{1}{2} \ln ( 1+x^2) +\]
anonymous
  • anonymous
my question is how do I do that
anonymous
  • anonymous
ohh yeh, now you have changed the question :|
anonymous
  • anonymous
sorry lol
anonymous
  • anonymous
add and subtract 1 on the top and bottom
anonymous
  • anonymous
\[=\frac{x^2+1-1}{x^2+1} = \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1} = 1- \frac{1}{x^2+1}\]
anonymous
  • anonymous
very basic, nothing really hard
anonymous
  • anonymous
nice
anonymous
  • anonymous
ok cool. sorry for me to make you feel angry lol

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