The graph below shows the function f(x)=5x+10/x^2+7x+10 where is the removable discontinuity of f(x) located?

For this case we have the following function:
  
 Let's rewrite the function:
 
 We set the denominator to zero to see the values of x for which it is not defined:
  
 From here, we get:
 
 There is a removable discontinuity at x = -2, since by rewriting the function we have:
  
 
 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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