Final answer:
The given mathematical expression, '(x^(-1)-3y^(-1))/(3y-9x)', simplifies to (1/x-1/(3y))/3(y-3x). This is achieved by understanding that a negative exponent implies the reciprocal of the base and by factoring out a common term in the denominator.
Step-by-step explanation:
To simplify the given mathematical expression, '(x^(-1)-3y^(-1))/(3y-9x)', we should first understand that a negative exponent means that we take the reciprocal of the base. So, x^(-1) is equivalent to 1/x and y^(-1) is equivalent to 1/y. So, the given expression becomes (1/x-1/(3y))/(3y-9x).
Next, let's factor the denominator, 3y-9x. We can factor out a 3 from each term to get 3(y-3x).
So, the simplified form of the given expression is (1/x-1/(3y))/3(y-3x). It's important to note that this simplification assumes that x, y, and (y-3x) are not equal to zero, as division by zero is undefined.
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