Question

what are the non-permissible value for the rational expression x^2 + x - 6 / x^2 + x -12?

a) x = 3 and x = -4
b) x = 0 and x = -4
c) x = 0 and x = -2
d) x = 2 and x = -3

Answer 1

The expression as written is not a rational expression. Parentheses are to be inserted to delimit the denominator and the numerator when more than one term is present:
x^2 + x - 6 / x^2 + x -12
should have been written as:
(x^2 + x - 6) / (x^2 + x -12)

To find the non-permissible values, factorize (if possible) the denominator and find where the denominator becomes zero. These are the non-permissible values. For example, the denominator factorizes to:
(x+4)(x-3)
So which are the values of x that will make the denominator zero?