Question 85436
First, multiply everything by x - 9:

(x - 9)({{{x/(x - 9)}}}) - 4(x - 9) = (x - 9){{{9/(x - 9)}}}

Denominators cancel out:

x - 4(x - 9) = 9

Distributive property:

x - 4x + 36 = 9

Combine like terms:

-3x + 36 = 9

Subtract 36 from both sides:

-3x = -27

Divide both sides by -3:

x = 9 [potentially]

Check for extraneous solutions [denominator can't = 0]:

x - 9 = 9 - 9 = 0.  Since this = 0, the solution x = 9 is extraneous. Since this is the only potential solution obtained to begin with, the equation has no solution.