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a) we are only concerned that the denominator not equal zero, therefore solve

x^2 + x - 6 = 0

(x+3)(x -2) = 0

x = -3, x = 2

Therefore the domain is (-infinity, -3)U(-3, 2)U(2, infinity)

b) here, inside the radical cannot be negative, therefore

9 - x^2 >_0

x^2 <_ 9

-3 <_x<_3

also, x - 1 >_0

x >_1

Combining, both solutions yields domain

[1, 3]

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