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What is the final answer for this: xy - 8/x^2y^2 ÷ x^2 - 4/y^2

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1 Answer

If the purpose is to simplify:
(lack of PARENTHESIS make this a guessing game, I'm going to assume that everything prior to the division symbol ÷ is in the numerator, and everything after is in the denominator)
[xy-8/x2y2]/[x2-4/(y2)]=[xy-8/x2y2]/[x2-4/y2] * [x2y2/x2y2]  Multiply the complex fraction by the LCD amongst all terms
                                 =[x3y3-8x2y2/x2y2]/[x4y2-4x2y2/y2]  Reduce
                                 =(x3y3-8)/(x4y2-4)  now factor
                                 =[(xy-2)(x2y2+2xy+4)]/[(x2y-2)(x2y+2)]  Difference of cubes/squares
                                 = (x2y2+2xy+4)/(x2y+2)
(Note: color function cut-out midway - I would really like to color code for greater understanding, but am at a loss to understand why Wyzants formatting isn't working here... it did for the first couple equations)