Question

this is a picture of my book, how did he get that for part a

http://prntscr.com/cwv21g

Answer 1

\[\frac{ 2x }{ x^2 -4 } +\frac{ 1 }{ x(x-2 }-\frac{ 1 }{ x-2 }\]

Answer 2

and the supposed answer is \[\frac{ x+1 }{ x( x+2)}\]

Answer 3

the farthest i got was \[\frac{ x^2 -x+2}{ x(x-2)(x+2) }\]

Answer 4

im past that already

Answer 5

I don't know how you got to where you are.

Did you rewrite the first term as:

2x²
------------
x (x+2)(x-2)

Answer 6

Did you rewrite the second term as:
(x+2)
------------------------
x (x+2)(x-2)

Answer 7

yes, then

Answer 8

I found the LCD and it was x(x-2)(x+2)

Answer 9

Did you write the third term as:

x(x+2)
-----------------
x (x+2)(x-2)

Answer 10

yes

Answer 11

the second was
x+2
---
x(x-2)(x+2)

Answer 12

2x² + (x+2) - x(x+2)
______________________
x (x+2)(x-2)

Answer 13

and expand the numerator

Answer 14

the numerator becomes 2x^2 +x+2-x^2 -2x

Answer 15

and then x^2 -x +2

Answer 16

x² - x + 2
----------
x (x+2)(x-2)

Answer 17

yup

Answer 18

but the book

Answer 19

Will this factor: x² - x + 2

Answer 20

no

Answer 21

There is a sign problem somewhere. I don't know if it is a book typo or an error I made.

Answer 22

i think book typo, i just checked this website https://www.symbolab.com/solver/equation-calculator/%5Cfrac%7B2x%7D%7Bx%5E%7B2%7D-4%7D%2B%5Cfrac%7B1%7D%7Bx(x-2)%7D-%5Cfrac%7B1%7D%7Bx-2%7D/?or=dym

Answer 23

I ran the problem through WolframAlpha and got the answer we did:

http://www.wolframalpha.com/input/?i=(2x)%2F(x%5E2+-4)+%2B+1%2F(x(x-2))+-+1%2F(x-2)+%3D

Answer 24

Yes. A typo is at play.

Did you work the second example?

Answer 25

yeah the second example is good

Answer 26

Okay.

Answer 27

thanks

Answer 28

You are welcome.
Your algebra skills are good.

Answer 29

thanks