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Find the domain of \(x^2 + 10x + 21/x^2 + 4x - 21\)  . (Express your answer using interval notation.)

tertre  Mar 12, 2017
 #1
avatar+86889 
0

(x^2 + 10x + 21) / ( x^2 + 4x + 21)

 

The domain will be undefined for any "x" that makes the denominator = 0

 

But

 

x^2 + 4x  + 21  = 0      has no real 0's

 

So....this rational function is defined everywhere ....  (-inf, inf)

 

See the graph, here : https://www.desmos.com/calculator/t3utixb7ot

 

 

cool cool cool

CPhill  Mar 12, 2017
 #2
avatar+86889 
+5

Oops....mis-read the denominator

 

x^2 +4x - 21    will have 0's  at

 

(x + 7) (x - 3)   = 0       set each factor to 0   and x = 3  or x = -7

 

So....the  domain  is  (-inf, -7) U (-7, 3) U (3, inf)

 

Thanks to hectictar and EP  for catching my error.....!!!!!

 

 

cool cool cool

CPhill  Mar 12, 2017

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