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