Question

Find the excluded values, of the following expression

`(x^3 - 27)/(x^3 + x^2 - 6x)`

Answer 1

`(x^3 - 27)/(x^3 + x^2 - 6x)`

x³ – 27 = x³ – 3³

= (x – 3) (x² + x + 3)

x³ + x² – 6x = x(x² + x – 6) = x (x + 3) (x – 2)

`(x^3 - 27)/(x^3 + x^2 - 6x) = ((x - 3)(x^2 + x + 3))/(x(x + 3)(x - 2))`

The expression `((x - 3)(x^2 + x + 3))/(x(x + 3)(x - 2))` is undefined

when x (x + 3) (x – 2) = 0

x = 0 or x + 3 = 0 or x – 2 = 0

x = 0 or x = – 3 or x = 2

The excluded values are 0 , – 3 and 2