SOLUTION: Can you give me a hand with this one? Thanks! x/x-2 = 2/x-3 Solve for x thanks!

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Question 61169This question is from textbook college algebra
: Can you give me a hand with this one? Thanks!
x/x-2 = 2/x-3 Solve for x
thanks! This question is from textbook college algebra

Answer by jai_kos(139) About Me  (Show Source):
You can put this solution on YOUR website!
x/x-2 = 2/x-3
Cross multiply the above term, we get
x(x-3) = 2(x-2)
x^2 – 3x = 2x – 4
x^2 -3x -2x + 4 = 0
x^2 – 5x + 4 = 0
x^2 – 4x –x + 4 = 0
x(x- 4) -1(x- 4) = 0
(x-4) (x-1) = 0
x = 4 or x =1