SOLUTION: Determine the values of x for any holes in the graph of f(x)= x + 3/ x^2 + 5x + 6

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Determine the values of x for any holes in the graph of f(x)= x + 3/ x^2 + 5x + 6      Log On


   

Question 324657: Determine the values of x for any holes in the graph of f(x)= x + 3/ x^2 + 5x + 6
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Holes or discontinuities occur when the denominator equals zero.
Some are removable depending on the numerator.
Factor the denominator first.
%28x%5E2%2B5x%2B6%29=%28x%2B3%29%28x%2B2%29
Since numerator and denominator share the factor %28x%2B3%29, the discontinuity is removable.
The only remaining discontinuity occurs when x%2B2=0 or x=-2.
Below is a graph of the original function showing the one discontinuity.
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graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B3%29%2F%28x%5E2%2B5x%2B6%29%29