To solve for x in the equation X-1/x=9 9/10, we first need to find a common denominator on the right side of the equation. The common denominator between 9 and 10 is 90 (9*10=90).

So, we rewrite the equation as:

(X*x - 1)/x = 99/10

Now, multiply both sides of the equation by x to get rid of the denominator:

X*x - 1 = 99x/10

Next, simplify:

10Xx - 10*1 = 99x

10x^2 - 10 = 99x

Rearrange the equation to set it equal to zero:

10x^2 - 99x - 10 = 0

This is now a quadratic equation. We can solve it by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in a = 10, b = -99, and c = -10:

x = (99 ± √((-99)^2 - 410(-10))) / 2*10

x = (99 ± √(9801 + 400)) / 20

x = (99 ± √10201) / 20

x = (99 ± 101) / 20

Therefore, x = (99 + 101) / 20 = 200 / 20 = 10 or x = (99 - 101) / 20 = -2 / 20 = -1/10

So, the solutions for x in the equation X-1/x=9 9/10 are x = 10 and x = -1/10.