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If ab > 0, then (a > 0 and b > 0) or (a < 0 and b < 0). This statment I can prove, just with the basic properties of numbers!

Then, 1[itex]/[/itex]b is defined as b[itex]^{-1}[/itex] right?

So, how does one prove that if [itex]\frac{a}{b}[/itex] > 0, then (a > 0 and b > 0) or (a < 0 and b < 0)?

Can you give me the complete proog of that? Thanks!

For example, how does one prove that if [itex]\frac{x+1}{x-1}[/itex] > 0, then

x > 1 or x < -1?

Regards,

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# Prove of Statement, Calculus, Basic Properties of numbers

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