reduce the expression(factor separately the numerator and the denominator, and then simplify; 5-x/x-5

If you mean to write:
5-x/x-5
then its
5-1-5=-1 as long as x is not 0
But if you mean:


then we notice that 5-x and x-5 are opposite in value. therefore their quotient is -1:


(as long as x does not equal -5)



Also notice that is just a coincidence that both expressions have the same value
:)