Please simplify.

5x ^-2 - 3y ^-1/
x ^-1 + y ^-1

The 5x is on top and the x^-1 is on the bottom

The first step is to remember that you can add exponents together. Then move everything into the numerator and add the exponets. this will give you your answer.

(5x^-2)-(3y^-1)
--------------- (original)
(x^-1)+(y^-1)

(5x^-2)+(x^1)-(3y^-1)+(y^1)

(5x^-1)-3 (-2+1=-1, and -1+1=0)

There is no division necessary here? So the final answer is what is @ the bottom?

(5x^-1)-3 (-2+1=-1, and -1+1=0)

To simplify the expression 5x^(-2) - 3y^(-1) / x^(-1) + y^(-1), we can apply the rules of exponentiation.

Let's rewrite the expression using positive exponents:

5 / (x^2) - 3 / y

Now, since we have a common denominator, we can combine the two fractions:

(5y - 3x^2) / (xy)

Therefore, the simplified expression is (5y - 3x^2) / (xy).