Two Newly Defined Functions

Algebra Level 2

xy=1x+1y,x#y=x+yxyx * y = \frac{1}{x} + \frac{1}{y}, \quad x \# y = \frac{x+y}{x-y}

Let the operations #\# and * be defined as described above.

Find the value of kk such that

(22k)#(k33)=27.(22 * k) \# (k * 33) = 27.

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