Question

(x^2+2x-3)/(x-2)<0

Answer 1

\[\frac{(x-1)(x+3)}{x-2}<0\] is where you start. the zeros are at -3, 1 and 2 so you will divide up the real line into 4 parts:
\[(-\infty, -3)\]
\[(-3,1)\]
\[(1,2)\]
\[(2,\infty)\]

Answer 2

you have only to check on one interval, because it will alternate between positive and negative so you will pick every other interval as your answer. i pick 0 which is in the interval
\[(-3,1)\] you can pick a different one to check if you like

Answer 3

ok dear thanks alot

Answer 4

can u represent it on a number line pls

Answer 5

you are welcome. we can finish if you like

Answer 6

replace x by 0 and get
\[\frac{-1\times 3}{-2}\] which is positive. so it will be negative on the interval
\[(-\infty,-3)\] and also on the interval
\[(1,2)\] and that is your answer

Answer 7

oh and 2 is not a zero
its where the expression is undefined

Answer 8

but everything else looks fine :)

Answer 9

ok

Answer 10

so my equality sign will be this (x/x<-3 or x<2)

Answer 11

?