Final Answer:
The simplified expression of 7x²−2x−9/((x²)(x−3)) is 7/(x−3), thus the correct option is a.
Explanation:
The given expression contains multiple operations, so we have to simplify it step by step. First, we need to simplify the numerator and denominator of the expression. In the numerator, the variable x is present in two terms, 7x² and -2x, so we can combine them by using the distributive property. Thus, 7x²−2x−9/((x²)(x−3)) becomes 7x-2-9/((x²)(x−3)).
Now, in the denominator, we can factorize x² and (x-3). We can see that (x-3) is a factor of the numerator also, so we can cancel it out from both the numerator and denominator. Therefore, 7x-2-9/((x²)(x−3)) simplifies to 7/(x-3). We can verify this answer by plugging in any value of x.