Question

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Answer 1

If f(x) = \[\huge \frac{ \frac{ 1 }{ x }+1}{ \frac{ 1 }{ x } -1}\]

Find the value of

f(x) + f(-x)

Answer 2

i just want to know what i should do for f(-x)

Answer 3

@Miracrown @wio

Answer 4

replace "x" by "-x"

Answer 5

oh i thought of that but i didn't want to take risk thanks

Answer 6

usually there always exist two method to solve these kind of problems :
1) easy+clever method
2) hard+dumb method

Answer 7

so what's the dumb method

Answer 8

hehe

Answer 9

:) you can guess the dumb method ! lets try a better method :

say :

\[\large f(x) = \frac{ \frac{ 1 }{ x }+1}{ \frac{ 1 }{ x } -1} = \dfrac{a}{b}\]

Answer 10

We know \(x\neq 0\), so might as well multiply by \(x/x\).

Answer 11

Notice that \(f(-x) = -\dfrac{b}{a}\)

Answer 12

Smart method is too complicated.

Answer 13

yes sry continue

Answer 14

add them both and simplify :

\[\dfrac{a}{b} - \dfrac{b}{a} = \dfrac{a^2 - b^2}{ab}\]

i think getting rid of fractions by multiplying x/x is a good idea

Answer 15

wio's suggestion :

\[\large f(x) = \frac{ \frac{ 1 }{ x }+1}{ \frac{ 1 }{ x } -1} = \dfrac{1+x}{1-x}\]

doesn't this look neat ?

Answer 16

yes

Answer 17

you're right !

Answer 18

well i got the answer anyhow

Answer 19

dumb method is more easier lol

Answer 20

lol the so called clever method had a serious mistake and its really not that clever o,o

Answer 21

This problem has no matter in it , but i don't know something is compelling me think about it more and harder

Answer 22

you keep throwing 'more' in front of superlatives...

Answer 23

go wid wio's suggestion, nothing to think harder... :)

Answer 24

ohk The answer is