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Question
Find the excluded values, of the following expression
`(x^3 - 27)/(x^3 + x^2 - 6x)`
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Solution
`(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
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