Answer:
The expression that is equivalent to the equation x^2+6x-27/x+9 is:
(x-3)
Explanation:
To explain why this expression is equivalent to the given equation, we can use the concept of factoring. Factoring is a method used to break down an expression or equation into its simplest form by finding common factors.
In this case, we can see that the expression x^2+6x-27 can be factored into (x+9)(x-3). We can determine this by looking for two numbers that multiply to give -27 (the constant term) and add up to give 6 (the coefficient of the x term). The numbers that satisfy this condition are 9 and -3.
Therefore, the original equation x^2+6x-27/x+9 can be rewritten as (x+9)(x-3)/(x+9). Notice that (x+9) cancels out, leaving us with (x-3) as the simplified expression.
So, (x-3) is equivalent to the given equation x^2+6x-27/x+9.