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x/2x-6-3/x^2-6x+9=x-2/3x-9

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1 Answer

x/(2x-6) - 3/(x^2-6x+9) = (x-2)/(3x-9) <==Is this what you want to solve?

Multiply both sides by the LCD: 6(x-3)^2,

3x(x-3) - 18 = 2(x-2)(x-3)

3x^2 - 9x - 18 = 2(x^2-5x+6)

Collect all terms in one side,

x^2 + x - 30 = (x+6)(x-5) = 0

Answer: x = -6, 5