SOLUTION: The rational expression (x^2+9x+k)/(x^2+5x-6), x is NOT equal to 1, -6 simplifies to (x+3)/(x-1) because k equals ....

 will simplify to  if and only if 
every value of x (other than 1 and -6) when substituted in both, gives the
same result.  Therefore, since 0 is the easiest possible number to substitute
for x, let's use it. [But any other number (other than 1 and -6) will work
just as well.  It just won't be as easy.]

Substituting x=0 in

 gives



which reduces to



Substituting x=0 in  gives

 

which reduces to

 

or 



Setting those equal:



   <--ANSWER

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Check by substituting k=18 in





Factoring numerator and denominator:



Canceling:



So it reduces to:



Edwin