Question

NEED HELP!
1 over x minus 2 over x squared minus x

Answer 1

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

Answer 2

Directions are to combine fraction and simplify if possible?

Answer 3

yes thats it!

Answer 4

First factor x^2-x
and let me know what you get

Answer 5

(x+x)(x-x)?

Answer 6

x-x=0
so (x+x)(0)=0
so x^2-x doesn't equal 0

Answer 7

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

Answer 8

Basically I see that x^2 and x have a common factor x
so x^2-x=x( what goes here )

Answer 9

x?

Answer 10

x(what)=x^2
x(what)=x

Answer 11

for the first blank it is x
that is x(x)=x^2
but x(what)=x?

Answer 12

x(1)=x

Answer 13

yes so you have
\[x^2-x \\ x(x-1)\]

Answer 14

since x(x)=x^2 and x(-1)=-x

Answer 15

\[\frac{1}{x}-\frac{2}{x(x-1)}\]
now the only way we will able to combine these fractions is if they have the same denominator

Answer 16

what factor are we missing on the bottom for the first fraction

Answer 17

x-1

Answer 18

yes
so we are going to multiply first fraction by (x-1)/(x-1)
like so
\[\frac{x-1}{x(x-1)}-\frac{2}{x(x-1)}\]

Answer 19

so now we can combine the fractions since they have the same bottom part

Answer 20

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

Answer 21

you can finish this up by replacing -1-2 with?

Answer 22

-3?

Answer 23

yah

Answer 24

\[\frac{x-3}{x(x-1)}\]
your answer could look like this
or they could have maybe remultiplied the bottom back to what it was

Answer 25

that is x(x-1) was x^2-x initially

Answer 26

i got it! thank you so much!

Answer 27

np