Please Simplify
5x^-2 - 3y^-1
--------------
x^-1 + y^-1
-(3x^2-5y) / (x(x+y))
Are you sure that is correct? Because I came up with this.
1. Write problem using positive exponents
2. Find the Least Common Denominator
3. Multiply the numerator and denominator by the LCD (xy)
4. Apply Distributive Property
5. Simplify
I agree with Bob
multiply top and bottom by (x^2)(y) to get his answer.
What about breaking the fractions a part like this?
5x -2 - 3y -1 = 5 - 3
-----------------
x -1 + y -1 -------
x^2 y
---------------------
1 + 1
------------
x y
= 5y+3x^2 * x^2 y
--------
x+y
x^2 y(5y+3x) = 5xy^2 + 3x^2 y
if you insist on doing it the hard way:
[5/x^2 - 3/y] / [1/x + 1/y]
= [(5y - 3x^2)/(x^2 y)]/[(y+x)/xy]
= [(5y - 3x^2)/(x^2 y)][xy/(x+y)]
= -(3x^2-5y) / (x(x+y))
which is Bob's answer, and which I also obtained in 1 step.