Find the zeroes of the function

f(x)= x^2-14x+48/x^2-64

Zeros of a function means that f(x) = 0

0 = (x^2-14x+48) / (x^2-64)

Multiply both sides by the denominator to cancel

0 = x^2-14x+48

Factor if possible, if not use the quadratic formula

0 = (x - 8) (x - 6)

Set each factor equal to zero

x-8 = 0

x = 8

AND

x-6 =0

x = 6

The zeros for the function are at x = 6 and x = 8.

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