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multiply both sides by (2-k)
5k = -7(2-k)
5k = -14 + k^2
a quadratic equation
0 = k^2 - 5k - 14
Factors to
(k-7)(k+2) = 0
two solutions
k = 7
k = -2, not valid, division by 0 in original equation
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Check solution of k=7 in original problem