Question

Rational expressions, again

Answer 1

hi dtdan

Answer 2

\[\frac{ 1-x^{-2} }{ (x-1)^{-2} }\]

Answer 3

i first factored out the denominator..?

Answer 4

x^2-2x+1

Answer 5

then im not sure

Answer 6

what's the rules for moving a term in a denominator to the numerator, etc?

Answer 7

move the bottom term up to the top with +2 exponent, then

Answer 8

1-x^4?<<numerator?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

final answer, including the denominator,

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

Answer 13

leave the x-1, x+1 as x^2-1 if you want

Answer 14

can you explain this

Answer 15

yeah

Answer 16

x^2 goes to the bottom i get

Answer 17

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

Answer 18

multiply, by x^2/x^2

Answer 19

1-1/x^2

Answer 20

numerator , i get that

Answer 21

\[\frac{ x^2 }{ x^2 }*(\frac{ 1 }{ 1 } - \frac{ 1 }{ x^2 }\]

Answer 22

then you get \[\frac{ x^2 }{ x^2 } - \frac{ 1 }{ x^2 } = \frac{ x^2 - 1 }{ x^2 } = \frac{ (x-1)(x+1) }{ x^2 }\]

Answer 23

your doing that to reduce terms?

Answer 24

to get rid of the fractions in the numerator

Answer 25

multiplied by the common denominator x^2

Answer 26

so this is the numerator..

Answer 27

yep

Answer 28

(x-1)^-2

what happens to the denominator ?

Answer 29

the negative term moves it up to the numerator

Answer 30

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

Answer 31

your allowed to just move terms up like that?

Answer 32

thats the concept i don't get

Answer 33

if it goes up, turns positive, goes down..turns negative?

Answer 34

right, when you switch sides of the fraction, you switch signes on the exponent

Answer 35

\[\frac{ 1 }{ a ^{-x} } = a^x\]

Answer 36

or
\[a ^{-x} = \frac{ 1 }{ a^x }\]

Answer 37

ahh i see. so now i should square out the (x-1)?

Answer 38

yeah , i wouldnt make the (x-1)^3, instead just combine the (x-1)(x+1) to (x^2 -1)

Answer 39

\[\frac{ (x-1)^2(x^2-1) }{ x^2 }\]

Answer 40

so now i just foil

(x^2-2x+1)(x^2-2x+1)

Answer 41

i would just leave it how it is

Answer 42

you could multiply out all the terms i guess, if you want to , but it will be more messy

Answer 43

the answer considers it more simplified after multiplying it out

Answer 44

(x^2-2x+1) * (x^2 - 1)

the second term doesnt do the expansion like you did

Answer 45

but im gonna do that and look over this problem..

i knew that x^-2 should be changed into a fraction before doing anything but no idea that you were suppose to multiply 1/1 by x^2

Answer 46

yeah just expand the (x^2-1) term and leave the first one alone

Answer 47

(x-1)^2* (x-1)(x+1)