Question

Please Simplify

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

Answer 1

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

Answer 2

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

Answer 3

I agree with Bob

multiply top and bottom by (x^2)(y) to get his answer.

Answer 4

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

Answer 5

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.

Answer 6

Thank you for all your help! :)

Answer 7

yea i agree with bob on his answer