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If something over 0 is undefined, and if a part of an equation satisfies this condition, and if x=2 is just equal to 1/x=1/2 by cross-multiplying, then (x ^ { 3 } + y ^ { 3 } ) = 0 is equal to 1 / ( x ^ { 3 } + y ^ { 3 } ) = 1/0 by cross-multiplying giving and equation of 1 / ( x ^ { 3 } + y ^ { 3 } ) - 1/0 = 0; after doing least common denominator the result would be [ 0 - ( x ^ { 3 } + y ^ { 3 })] / 0 =0 which is - ( x ^ { 3 } + y ^ { 3 } ) /0 = 0, but it should not be equal to zero but undefined? Though if you solve it properly there are many solutions for this. Does it mean that all equations equal to 0 is undefined at the same time having a solution set? If not please explain why.
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