SOLUTION: Hello, good morning. I need help with this math problem. It says: "Simplify: [(2x^-1)+(3y^-1)]/[(9x^2)-(4y^2)]" Could you explain it to me step by step? Thank you in advance.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, good morning. I need help with this math problem. It says: "Simplify: [(2x^-1)+(3y^-1)]/[(9x^2)-(4y^2)]" Could you explain it to me step by step? Thank you in advance.      Log On


   

Question 944523: Hello, good morning. I need help with this math problem.
It says: "Simplify: [(2x^-1)+(3y^-1)]/[(9x^2)-(4y^2)]"
Could you explain it to me step by step?
Thank you in advance.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
[(2x^-1)+(3y^-1)]/[(9x^2)-(4y^2)]
((2x^-1)+(3y^-1))/((9x^2)-(4y^2))

%28%282x%5E-1%29%2B%283y%5E-1%29%29%2F%28%289x%5E2%29-%284y%5E2%29%29

%282%2F%28x%29%2B3%2Fy%29%2F%28%283x-2y%29%283x%2B2y%29%29

%28%282y%2B3x%29%2F%28xy%29%29%2F%28%283x-2y%29%283x%2B2y%29%29, note an oppurtunity for commutative property of equality in the numerator.

%28%283x%2B2y%29%2F%28xy%29%29%2F%28%283x-2y%29%283x%2B2y%29%29

%28cross%28%283x%2B2y%29%29%2F%28xy%29%29%2F%28%283x-2y%29cross%28%283x%2B2y%29%29%29

%281%2F%28xy%29%29%2F%283x-2y%29, a complex fraction still, and you can multiply by %28xy%29%2F%28xy%29 to get...

highlight%281%2F%28%28xy%29%283x-2y%29%29%29, and to finish actually "simplifying", do the multiplication indicated in the denominator.

highlight%281%2F%283x%5E2y-2xy%5E2%29%29


Other than those, the sequence of steps to take are understandable and should not need explanation for which to choose in sequence.