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\(\text{Find the domain of $\frac{x^2 + 10x + 21}{x^2 + 4x - 21}$. (Express your answer using interval notation.) }\)

 

Thanks!

 Jul 16, 2019
 #1
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The domain is only affected by the values of x that make the denominator 0

 

So....set   x^2 + 4x - 21  = 0  to find these values

 

Factor as

 

(x + 7) ( x - 3)  = 0        set each factor to 0   and solve for x   and we have

 

x + 7  = 0                   x - 3  = 0

 

x  = - 7                        x  =  3

 

 

So  the domain is all x except  x  = -7  and x =  3

 

In interval notation

 

( - infinity, -7)   U  (-7, 3)   U   ( 3, infinity )

 

 

 

cool cool cool

 Jul 16, 2019

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