SOLUTION: does y=(2x^2+3x+1)/(x^2-5x+4) have a hole

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Question 611295: does y=(2x^2+3x+1)/(x^2-5x+4) have a hole
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
y=%282x%5E2%2B3x%2B1%29%2F%28x%5E2-5x%2B4%29
A rational function will have a hole if there is a common factor between the numerator and denominator. (If there is more than one common factor, then there there will be that many holes.)

So we need to see what the factors of the numerator and denominator are:
y=%28%282x%2B1%29%28x%2B1%29%29%2F%28x-1%29%28x-4%29%29
There are no common factors between the numerator and denominator so there will be no holes in the graph.