SOLUTION: {{{((x-1)/(x^2-5x+6))+((x)/(x-2))=((2)/(x-3))}}} I need steps and answer! Thanks!

Question 699533:
I need steps and answer! Thanks!
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!

Factor the 1st denominator

we can multiply thru be (x-2)(x-3) and get rid of the denominators, resulting in:
(x-1) + x(x-3) = 2(x-2)
:
x - 1 + x^2 - 3x = 2x - 4
Combine like terms on the right
x^2 + x - 3x - 2x + 4 = 0
A quadratic equation
x^2 - 4x + 4 = 0
Factors to
(x-2)(x-2) = 0
x = 2, however this cannot be a solution,
Substitute 2 for x, the 1st and 2nd denominators would have division by 0

Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!

I need steps and answer! Thanks!

**Note: , or , as these values would render the equation UNDEFINED

x - 1 + x(x - 3) = 2(x - 2) ------ Multiplying by LCD, , or (x - 2)(x - 3)

(x - 3)(x - 1) = 0

x - 3 = 0 ------ x = 3 (ignore as it was stated before that: )

OR

x - 1 = 0 -----

You can do the check!!

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