The expression (x³ - 27) ÷ (x⁴ + 3x³ - 27x - 81) when simplified is 1/(x + 3)
How to simplify the expression
From the question, we have the following parameters that can be used in our computation:
(x³ - 27) ÷ (x⁴ + 3x³ - 27x - 81)
Simplifying the divisor, we have
(x³ - 27) ÷ (x³(x + 3) - 27(x + 3))
Factor out x + 3
So, we have
(x³ - 27) ÷ ((x³ - 27)(x + 3))
Cancel out the common factor
This gives
1/(x + 3)
Hence. the expression when simplified is 1/(x + 3)