Respuesta :

carlosego
For this case we have the following function:
 [tex] f (x) = (5x + 10) / (x ^ 2 + 7x + 10) [/tex] 
 Let's rewrite the function:
 [tex] f (x) = (5x + 10) / ((x + 2) (x + 5)) f (x) = (5 (x + 2)) / ((x + 2) (x + 5))[/tex]
 We set the denominator to zero to see the values of x for which it is not defined:
 [tex] (x + 2) (x + 5) = 0 [/tex] 
 From here, we get:
 [tex]x = -2 x = -5 [/tex]
 There is a removable discontinuity at x = -2, since by rewriting the function we have:
 [tex] f (x) = 5 / (x + 5) [/tex] 
 Answer:
 the removable discontinuity of f (x) is located at:
 x = -2
The correct answer is x= - 2.

Explanation:
A removable discontinuity happens where y=(0/0). To find this, we first factor the numerator and denominator.

For our numerator, we factor out the GCF; 5 is the GCF. Factoring 5 out of 5x leaves x, and factoring 5 out of 10 leaves 2, which gives us 5(x+2).

To factor the denominator, we want factors of c, 10, that sum to b, 7. 5*2=10 and 5+2=7, so this gives us (x+5)(x+2).

Next we find the common factors in the numerator and denominator; (x+2) is the common factor. We set this equal to 0: x+2=0. Now we solve for x by subtracting 2 from each side: x+2-2=0-2; x= - 2.  

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