SOLUTION: Solve: x/x-9 -4=9/x-9

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve: x/x-9 -4=9/x-9      Log On


   

Question 85436: Solve:
x/x-9 -4=9/x-9
Answer by scianci(186) About Me  (Show Source):
You can put this solution on YOUR website!
First, multiply everything by x - 9:
(x - 9)(x%2F%28x+-+9%29) - 4(x - 9) = (x - 9)9%2F%28x+-+9%29
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.