Question

Need help please!
http://i.imgur.com/hOzVQ7n.jpg
Can anyone help me find out what I did wrong on # 9?
what i did:
http://i.imgur.com/acYxvWM.jpg
http://i.imgur.com/m1ZZ1R5.jpg

Answer 1

number 9 ?

Answer 2

yep! sorry, shulda specified

Answer 3

i cant get my answer to look like the final one :<

Answer 4

well you did a ton of extra work for sure

Answer 5

yeahT__T

Answer 6

first off \(f(2)=1\) right ?

Answer 7

yes xD

Answer 8

so we start with
\[\frac{\frac{1}{\sqrt{x-1}}-1}{x-2}\]

Answer 9

remove the annoying fraction within a fraction by multiplying top and bottom by \(\sqrt{x-1}\)

Answer 10

leave it in factored form, don't multiply out

Answer 11

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

Answer 12

ohh. i see that part. i factored it. :< but what else do i need to do? I need the numerator to be a one

Answer 13

ok then if you need that multiply by the conjugate of \(1-\sqrt{x-1}\)which is \(1+\sqrt{x-1}\)

Answer 14

leave the denominator in factored form, don't multiply out

Answer 15

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

Answer 16

now the numerator is \(2-x\) and in the denominator you have \(x-2\) and
\[\frac{2-x}{x-2}=-1\]

Answer 17

ooooo. i see it :D

Answer 18

how you were supposed to know to do this i have no idea, unless it said "rationalize the numerator"

Answer 19

thanks xD!!! now i kno not to multiply my stuff too much.

Answer 20

oh, but thanks anyway :D

Answer 21

yeah this looks like the beginning of calculus, because this is a difference quotient

Answer 22

yeah it is. :< im in calc AB

Answer 23

then look to cancel, so don't multiply out
anyway this is algebra, just messy

Answer 24

alright. xD