Please simplify.
5x ^-2 - 3y ^-1
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x ^-1 + y ^-1
see michelle's answer
I got (5x^-1)-3
To simplify the expression, we need to apply the rules of exponents.
First, let's rewrite the expression using positive exponents. We can do this by moving any term with a negative exponent to the other side of the fraction by changing the sign of the exponent:
(5 / x^2 - 3 / y) / (1 / x + 1 / y)
Next, let's simplify the expression by multiplying the numerator and denominator by the common denominator, which in this case is xy:
[(5 / x^2 - 3 / y) * xy] / (1 / x + 1 / y) * xy
Now, simplify each term:
[(5y - 3x) / x^2y] / [(y + x) / xy]
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
[(5y - 3x) / x^2y] * [xy / (y + x)]
Simplify by canceling out common terms:
[(5y - 3x) * (xy)] / (x^2y * (y + x))
Multiply the terms:
(5xy^2 - 3x^2y) / (x^2y^2 + xy^3)
That's the simplified expression.