SOLUTION: Find the real number restrictions on x in the expression: x^2/x^2-14x+49

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Question 90539: Find the real number restrictions on x in the expression:
x^2/x^2-14x+49
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Set the denominator equal to zero (remember: dividing by zero is not allowed)

x%5E2-14x%2B49=0

%28x-7%29%28x-7%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:

x-7=0 or x-7=0

x=7 or x=7 Now solve for x in each case

Since these two answers are the same, our only answer is x=7

Since x=7 makes the entire denominator equal to zero, this means x=7 is excluded from the domain.


Notice if we graph x%5E2%2F%28x%5E2-14x%2B49%29 we get

+graph%28+500%2C+500%2C+-5%2C+15%2C+-5%2C+15%2C+x%5E2%2F%28x%5E2-14x%2B49%29%29+

and we can see that there is a discontinuity at x=7, so this verifies our answer.