The function f (x) = 7x-m/2-nx, find the values of m and n such that the vertical asymptote is x=6, and the x-intercept is 5.

The function is f (x) = (7x-m) / (2-nx)

the vertical asymptote is x=6, that means 2/n = 6 or n=1/3

And now, we have f (x) = (7x-m) : (2-1/3x) = (14x-2m) : (6-x)

the x-intercept is 5 and we have y=0, x=5. So we obtain 0 = (70-2m) : (6-5)

or 70-2m=0, m=35

Conclusion m=35 and n=1/3