For which values of $k$ does the equation $\frac{x-1}{x-2} = \frac{x-k}{x-6}$ have no solution for $x$? Enter all the possible values of $k,$ separated by commas.
Wait I thought of another one, if you use k = 6, then the equation will be x-1=x-2, that means -1=-2, which has no solutions, so k= 5, 6, and Idk if there are more
+128475 x - 1 x - k
____ = _______
x - 2 x - 6
Cross-multiply
x^2 - 7x + 6 = x^2 - 2x -kx + 2k
When k = 5 we have no solutions because we will end up with
6 =10 which is impossible
Also...when k = 6 the rational function on the right will have the graph of the line y = 1 (with a "hole" at x = 6)
But the rational function on the left will have a horizontal asymptote at y =1.....so these functions will never intersect when k = 6
So....no solutions when k= 5 or k = 6
