SOLUTION: Hi I have to solve the following rational inequality: 2/x+1 <= 4/x-3 The first thing I did was to set it to 0. 2/x+1 - 4/x-3 <= 0 Then I multiplied by the lcd: 2(x-3)-4(x+1)/(

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Question 848585: Hi I have to solve the following rational inequality:
2/x+1 <= 4/x-3
The first thing I did was to set it to 0.
2/x+1 - 4/x-3 <= 0
Then I multiplied by the lcd:
2(x-3)-4(x+1)/(x-3)(x+1)
Then I combined the numerator's like terms and placed that over the lcd:
-2x-10/(x+1)(x-3)<= 0
Then I set each part equal to 0.
x-3=0, x+1=0, -2x-10=0
So i got x= 3, x=-1, x=-5
Then I put it on a number line, which broke it up into 4 intervals
(-infinite, -5), (-5,-1), (-1,3), (3,infinite)
I found that in testing possible intervals that the two intervals that worked were (-infinite, -5] and [3, infinite)
I was wondering if I did this correctly, and did I need to set up restrictions? Thank you for any help!!!!!
Found 2 solutions by ewatrrr, richwmiller:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

y =

x = -5,a root.   Good Work.

Note:  asymptotes:  x = -1  and x = 3

Graphing:  x = [5,-1) U (3,∞ )



 

Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
 Not quite right



(x+5)/((x-3) (x+1))>=0

x>3

-5<=x<=-1

That is two intervals

greater than 3 and 

from greater than -5 to less than -1 

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