xy - 8/x

^{2}y^{2 }÷ x^{2}- 4/y^{2}xy - 8/x^{2}y^{2 }÷ x^{2} - 4/y^{2}

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Simi Valley, CA

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/x^{2}y^{2}]/[x^{2}-4/(y^{2})]=[xy-8/x^{2}y^{2}]/[x^{2}-4/y^{2}] * [x^{2}y^{2}/x^{2}y^{2}] Multiply the complex fraction by the LCD amongst all terms

=[x^{3}y^{3}-8x^{2}y^{2}/x^{2}y^{2}]/[x^{4}y^{2}-4x^{2}y^{2}/y^{2}]
Reduce

=(x^{3}y^{3}-8)/(x^{4}y^{2}-4) now factor

=[(xy-2)(x^{2}y^{2}+2xy+4)]/[(x^{2}y-2)(x^{2}y+2)] Difference of cubes/squares

= (x^{2}y^{2}+2xy+4)/(x^{2}y+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)

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