Math Help Please!!?

Question

How do you solve this problem?? Thanks.

For what value of "k" will the solution set of (4x-k)/(x-5) = 3 be the empty set?

Answer 1

4x-k = 3x-15, multiplying out
Then x = -15+k
If k=15, you have 0=0. That's pretty empty.

Answer 2

The empty solution is {}, solutions to x = 0 are {0}.

By multiplying out, and isolating x you get x = k -15.
If k = 20, then x = 5.
However x can not equal 5, because then the denominator in the original equation is undefined. Thus for k = 20, there is no solution.