To solve the first equation, X-7/x+5 = 2, we need to find a common denominator:

(X^2 - 7x) / (x+5) = 2

Cross multiply:

X^2 - 7x = 2(x+5)
X^2 - 7x = 2x + 10
X^2 - 9x - 10 = 0

Now, solve for X using the quadratic formula:

X = [9 ± √(81 + 40)] / 2
X = [9 ± √121] / 2
X = [9 ± 11] / 2

So, X = 10 or X = -1.

Now, for the second equation, x+5/4x-2/3=x-9/6:

This is a bit unclear without parentheses to show how the equation should be interpreted.

If the equation is (x+5)/(4x-2)/3 = x-9/6, then it simplifies to x/4x-2 = x-3/6 which can be further simplified to 1/(4x-2) = 1/6.

Solving for x we get:

4x - 2 = 6
4x = 8
x = 2

If you have a different interpretation of the equation, please clarify or provide parentheses to make it clear.