x^2/(x- 9 = 81/(x - 9)
This is the equation for which you want the solution.
Multiplying both sides of the equation by (x - 9) we get
x^2(x - 9)/(x - 9) = 81(x - 9)/(x - 9)
So the (x - 9) goes out from both the denominator and the numerator and then the simplified equation becomes
x^2 = 81
x ^2 = (9)^2
x = 9
So the value of the unknown variable x comes out to be 9.