$$f(x)=\frac{ x^2-4 }{x^2-7x+10 }=$$ Use interval notation to indicate where f(x) is continuous.
Interval(s) of Continuity:

Question

$$f(x)=\frac{ x^2-4 }{x^2-7x+10 }=$$                   Use interval notation to indicate where f(x) is continuous.
Interval(s) of Continuity:

anteater · Answer

Factor numerator and denominator:
Numerator:   x^2 - 4 = (x + 2)(x - 2)
Denominator:  x^2 - 7x + 10 = (x - 5)(x - 2)  

There are discontinuities at x = 5 and x = 2, since those would cause division by 0. Since (x -2) is a factor in both the numerator and the denominator, there is a "hole", or removable discontinuity, in the graph of your function at x = 2.

There is a vertical asymptote at x=5.

f(x) is continuous on the intervals: $$\left( -\infty,2 \right)\cup(2,5)\cup(5,\infty)$$