+0  
 
-1
21
1
avatar+1123 

Help can someone explain this.  I think the answer is no real numbers, but that's wrong.

 

Solve the inequality
\[\frac{x^2 - 25}{x + 5} < x + 5.\]

 Aug 7, 2023
 #1
avatar+126978 
+1

Factor the numerator on the  left side

 

[ (x + 5) ( x - 5) ] / (x + 5)  < x + 5     simplify

 

x  - 5  <  x + 5

 

This is true  for  all real  numbers   except for  x  = -5  (because looking back  at the  original problem, it  makes the  denominator on the  left = 0 )

 

So  x< -5   and  x >  -5

 

cool cool cool

 Aug 7, 2023

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