Question

The fraction (1+(1/x))/(1-(1/x^2)) is equivalent to...
please explain how you get your answer.

Answer 1

\[\frac{ 1+\frac{ 1 }{ x } }{ 1-\frac{ 1 }{ x ^{2} } }\]

thats the fraction if it makes it easier^

Answer 2

are you supposed to get rid of the fraction?

Answer 3

i mean turn it into a non fraction?

Answer 4

no you are supposed to simplify the fraction

Answer 5

ok so what is the least common denominator? for everything?

Answer 6

x?

Answer 7

close,

Answer 8

still missing something

Answer 9

\[x^{2}\]

Answer 10

?

Answer 11

correct

Answer 12

so multiply each numerator and denominator by whats needed to get x^2 as the denominator for each term, 2 terms up top, 2 terms on bottom

Answer 13

and you should get a fraction plus a fraction divided by a fraction minus a fraction

Answer 14

each of the 4 fractions will have x^2 as the denominiator

Answer 15

post that when you have it

Answer 16

you know what i mean?

Answer 17

ok guess not?

Answer 18

im sorry i understand my computer just freaked out on me but i got it working again

Answer 19

oh ok

Answer 20

so\[\frac{ \frac{ x ^{2} }{ x ^{2} }+\frac{ x }{ x ^{2} } }{ \frac{ x ^{2} }{ x ^{2} }- \frac{ 1 }{ x ^{2} } }\]?

Answer 21

thats correct, now combine the fractions in the numerator and combine the fractions in the denominator

Answer 22

ok so...\[\frac{ \frac{ x ^{2}+x }{ x ^{2} } }{ \frac{ - x ^{2} }{ x ^{2} } }\]?

Answer 23

the top looks right, but the bottom is (x^2 -1)/(x^2)

Answer 24

after fixing that, invert and multiply the denominator and cancel the x^2's and then factor the new denominator, and cancel as necessary

Answer 25

oh ok so...\[\frac{ \frac{ x(x+1) }{ x ^{2} } }{ \frac{ (x+1)(x-1) }{ x ^{2} } }\]
then...\[\frac{ \frac{ x }{ x ^{2} } }{ \frac{ x-1 }{ x ^{2} } }\]?
then what?

Answer 26

is that right?

Answer 27

thats right but you can cancel out the x^2 leaving you with x/(x-1)

Answer 28

remember though they are only equal when x != 0 and x != 1

Answer 29

or is it...\[\frac{ x(x+1) }{ x ^{2} }\times \frac{ x ^{2} }{ (x+1)(x-1) }\]
then you cross out (x+1)s and the x^2s and get...
\[\frac{ x }{ (x+1) }\]

Answer 30

thank you so much

Answer 31

i meant \[\frac{ x }{ x-1 }\]

Answer 32

yw :)