Question 117015
{{{((x+7)/(x-7))/((x^2-49)/(7-x))}}} Start with the given expression



{{{((x+7)/(x-7))((7-x)/(x^2-49))}}} Multiply the first fraction by the reciprocal of the second fraction



{{{((x+7)/(x-7))((7-x)/((x+7)(x-7)))}}}   Factor {{{x^2-49}}} to get {{{(x+7)(x-7)}}} 



{{{(x+7)(7-x)/(x-7)(x+7)(x-7)}}} Combine the fractions


{{{-(x+7)(x-7)/(x-7)(x+7)(x-7)}}} Factor a -1 out of {{{7-x}}} to get {{{-1(x-7)}}}



{{{-cross((x+7))cross((x-7))/(x-7)cross((x+7))cross((x-7))}}} Cancel like terms



{{{-1/(x-7)}}} Simplify



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Answer:


So {{{((x+7)/(x-7))((7-x)/(x^2-49))}}} simplifies to {{{-1/(x-7)}}}. In other words {{{((x+7)/(x-7))((7-x)/(x^2-49))=-1/(x-7)}}}