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dividing complex fractions

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1 Answer

E = (9/x + 7/x^2)/(5/y + 3/y^2)

Can’t divide by zero, so x≠0 and y≠0.
xy≠0 includes both.

Multiply right side by 1=(x^2y^2)/(x^2y^2):

E = (9x^2y^2/x + 7x^2y^2/x^2)
/(5x^2y^2/y + 3x^2y^2/y^2), xy≠0

E = (9xy^2 + 7y^2)/(5x^2y + 3x^2), xy≠0

E = y^2(9x+7)/(x^2(5y+3)), y≠0

[Try substituting y=0 in original and final E. The result should be the same, right?]