Question

Please find attached.

Answer 1

multiply both sides by (x-1)
what is true of the result?

Answer 2

hollywood!

Answer 3

@satellite73 I have already solved it, but one of my answers is wrong.

Answer 4

you cannot multiply both sides by \(x-1\) because you do not know if \(x-1>0\) or \(x-1<0\)

Answer 5

you have to subtract \(3x+5\) from both sides, add the fractions, and then solve
it is a real pain in the neck

Answer 6

Ah..

Answer 7

\[\frac{(x+3)(x+9)}{x-1}-3x+5>0\] is a start

Answer 8

How about setting equal, then solving, then finding in which domains of x between zeroes it is > or < 0?

Answer 9

this really is a drag, you have to add up the fraction

Answer 10

For example, I set the two sides equal, then factored into
(x-11)(x+1).

Answer 11

@satellite73 the multiple out the brackets right.

Answer 12

\[x^2+12x+27/x-1 - 3x-5(x-1)/x-1\]

Answer 13

\[(x-11)(x+1)/x-1\]

Answer 14

\[\frac{(x+3)(x+9)}{x-1}-3x+5>0\]
\[\frac{(x+3)(x+9)-(x-1)(3x-5)}{x-1}>0\]
\[\frac{-2x^2+20x+22}{x-1}>0\]
\[\frac{-2(x^2-10x-11)}{x-1}>0\]divide by -2 and change the sign
\[\frac{x^2-10x-11}{x-1}<0\] factor
\[\frac{(x-11)(x-1)}{x-1}<0\] and finally we are ready to solve

Answer 15

yeah what you wrote! but notice that the inequality has been switched from \(>0\) to \(<0\)

Answer 16

also i have a typo, it should be \[\frac{(x-11)(x+1)}{x-1}<0\]

Answer 17

@waterineyes you say "mistake" is say "typo"
po tay to
po tah to

Answer 18

sick guys.

Answer 19

I think you took it seriously @satellite73

Answer 20

thanks @satellite73

Answer 21

oh no i always call my errors "typos" ask myininaya

Answer 22

sometimes they even are typos, but mostly they are just garden variety mistakes

Answer 23

@Hollywood_chrissy now you are good to go right? changes sign at \(x=-1,1,11\) and is negative if \(x<-1\) or \(1<x<11\)

Answer 24

yessir

Answer 25

btw good to see you back. this is much harder math than before right? you must have been doing lots of work

Answer 26

:)

Answer 27

yes it is.