+0  
 
+1
67
3
avatar

Can anyone help with this?

 

solve (x + 1)/(x^2 -4 ) > 0

 Jun 2, 2020
 #1
avatar+23 
0

Factor the denominator to get

(x+1)/[(x+2)(x-2)]

and then check what happens around all the critical points (-2, -1, 2) to see that the solution is (in interval notation):

(-2, -1) U (2, ∞)

 

Hope this solution helps!

 Jun 2, 2020
edited by North  Jun 2, 2020
 #2
avatar+25820 
+3

First of all   x cannot = 2  or  -2   because the denominator would be zero....not allowed

  the denomintor factors to  (x-2)(x+2)

 

(x+1) /  (x-2)(x+2)   >0            so look at the intervals from   - inf to -2     then   -2  to -1    then   -1 to 2   then  2 to +inf

                                                                                                    <0                        >0                      <0                >0

 

 

so   x can be        (-2,-1) U (2, + inf)          (remember x cannot = 2 or -2    and at x = -1 the fxn = 0            

 Jun 2, 2020
 #3
avatar+23 
+1

You are right, I made a mistake. Sorry!

North  Jun 2, 2020

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