J K Flip Flop and Boolean Algebra
Start with the original equation:

Y = K'J'Q + K'J + KJQ'

The trick is to create two terms that are equivalent to the middle term, using the fact that X + X' = 1:

Y = J'K'Q + JK'(Q + Q') + JKQ'

Y = J'K'Q + JK'Q + JK'Q' + JKQ'

Now factor the pairs of terms:

Y = K'Q(J + J') + JQ'(K + K')

Simplify, again using the fact that X + X' = 1:

Y = K'Q + JQ'

This is really obvious if you draw the Karnaugh map for the function. The JK' term is redundant, given the other two terms.