Question

What did I do wrong trying to simplify this rational exponent?

Answer 1

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

Answer 2

For the numerator here is what I did

Answer 3

\[\frac{ 1 }{ y^2 }-\frac{ y^2 }{ y^2 }\]

Answer 4

then finally i got\[\frac{ 1-y^2 }{ y^2(1+y) }\]

Answer 5

^^y^3 sorry

Answer 6

\[\frac{ 1-y^2 }{ y^2+y^3 }\]

Answer 7

then what do i do?

Answer 8

it looks good to me

Answer 9

you have simplified completely, if you want to separate the fractions you can, but no need....

Answer 10

I see what you did;it's all good.

Answer 11

the answer is however
\[\frac{ 1-y }{ y^2 }\]

Answer 12

you can factor the 1-y^2 using the difference of squares rule

Answer 13

you'll find something cancels

Answer 14

oh word

Answer 15

difference of squares: \(\large\color{black}{ a^2-b^2=(a-b)(a+b) }\)

Answer 16

and factor the bottom out of \(\large\color{black}{ y^2 }\)

Answer 17

(1-y)(1+y)

Answer 18

for the top, yes

Answer 19

and factoring the bottom you get?

Answer 20

y^2(1+y)

Answer 21

cross out the 1+y

Answer 22

yup

Answer 23

the new fraction will look like?

Answer 24

you had: \(\large\color{black}{ \frac{\LARGE (y-1)(y+1)}{\LARGE y^2(y+1)} }\)

Answer 25

and now it becomes?

Answer 26

y-1/y^2

Answer 27

yes

Answer 28

\(\large\color{black}{ \frac{\LARGE y-1}{\LARGE y^2} }\)

Answer 29

any one go to connections?

Answer 30

this is considered to be a spam (most likely)

Answer 31

I don't, btw

Answer 32

alright thanks. it seems like im getting most of it, but im always missing one important step..

Answer 33

anyone makes mistakes, it happens. I have even the silliest mistakes that can possibly be sometimes...

Answer 34

i see how. i have a quick concept question

Answer 35

sure

Answer 36

if i have a negative exponent on the denominator...turns positive in the numerator, vice versa..?

Answer 37

\(\large\color{black}{ a^{\LARGE -b}=\frac{\LARGE 1 }{\LARGE a^{b}} }\)

Answer 38

therefore:

\(\large\color{black}{ \frac{\LARGE 1 }{\LARGE a^{-b}}= \frac{\LARGE 1 }{\frac{\LARGE 1}{\LARGE a^{b}}}=a^b }\)

Answer 39

(you are correct)

Answer 40

im not sure what you drew out looks like a complex fraction

Answer 41

it is 1 over a fraction (between the equal signs in latex)