Question 1083402
1/(2x-6), I am assuming the parentheses belong
When k is added to x,  it is 1/(2(x+k)-6)=1/(2x+2k-6)
this equals 1/(2x-4)
therefore, 2x+2k-6=2x-4
2k=2, k=1, ANSWER

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(1/2)x-6 with (x+k)=(1/2)(x+k)=(1/2)(x)-4
(1/2)x-(1/2)k=(1/2)x-4
k=4 ANSWER
(1/2)(x+4)-6=(1/2)x+2-6=(1/2)x-4