Question 1063160
I'll use substitutions to make it clearer,
{{{A=x+y}}}
{{{B=x-y}}}
{{{-B=y-x}}}
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{{{((x-y)/(x+y))/((y-x)/(y+x))=(B/A)/(-B/A)}}}
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Dividing by a fraction is equivalent to multiplying by its reciprocal,
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{{{((x-y)/(x+y))/((y-x)/(y+x))=(B/A)*(-A/B)}}}
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{{{((x-y)/(x+y))/((y-x)/(y+x))=-1}}}