Find all real numbers k such that the limit exists

Question

Find all real numbers k such that limit lim->3 1/x-1/k/3x-9 exists

Answer 1

Amber, this is a case of removable discontinuity

1/x-1/k/3x-9 same as {-(x-k)/(3*k*x*(x-3)]

if k=3 the the expression becomes -1/9x which when x approaches 3 has a limit

that equals the value of the expression, -1/27

k=3 is the only value I find making the limit defined