Question

express in simplest form:

1 - 1/x
---------
x - 2 + 1/x

Answer 1

\[\frac{1-\frac{1}{x}}{x-2+\frac{1}{x}}\] like that?

Answer 2

yes like that

Answer 3

clear the compound fraction by multiplying numerator and denominator by \(x\), takes one step

Answer 4

huh

Answer 5

multiply top and bottom by \(x\)

Answer 6

\[\frac{1-\frac{1}{x}}{x-2+\frac{1}{x}}\times \frac{x}{x}\] is the first step

Answer 7

you are allowed to do this because \(\frac{x}{x}=1\)
it is just a trick to clear the denominators

Answer 8

so its gonna be
x−1
---------
x^2−2x+1

Answer 9

the you factor ?
9x-1)(x-1)

Answer 10

(x-1) *

Answer 11

\[\frac{x-1}{x^2-2x+1}=\frac{x-1}{(x-1)(x-1)}=\frac{1}{x-1}\] i guess that is right