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do i multiply both sides by x-1?
Yea. Do the opposite.
No... this is a rational expression inequality. So you need to think about the SIGN of the rational expression in different parts of the domain.
Listen to DebbieG
Then find the regions where the ratio is > or = 0 Since it's a ratio, it will potentially change sign anywhere that either the num'r or den'r has a root. So those points "divide up" your domain.
Where is x - 3=0? Where is x + 1=0?
good.... so you can divide up the domain like so: |dw:1377816164909:dw|
Hold on, not that simple. Think about the sign of each factor (num'r and den'r each have one factor) in each part of the domain.
When x<-1: is the num'r positive or negative? is the den'r positive or negative?
(You can just plug in a test number, like x=-2)
Find the sign in each region of the domain - remember, the sign of the RATIO depends on whether the two factors have the SAME or DIFFERENT signs.
Then construct your solution set, also keeping in mind what is happening at the partition points: At x=-1, function is UNDEFINED At x=3, function is =0 So x=3 is IN the solution set. x=-1 is NOT.
theres an asymptote at x=-1
Yeah, graphical methods can be useful also. It kind of depends on what you've studied so far about rational equations. Also whether you are expected to do this type of problem with a calculator (I wouldn't blink about giving this problem in my Algebra 2 class on a NON-calculator quiz or exam).
debbie u teach highschool?