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

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: {{{((x-1)/(x^2-5x+6))+((x)/(x-2))=((2)/(x-3))}}} I need steps and answer! Thanks!      Log On


   

Question 699533: %28%28x-1%29%2F%28x%5E2-5x%2B6%29%29%2B%28%28x%29%2F%28x-2%29%29=%28%282%29%2F%28x-3%29%29
I need steps and answer! Thanks!
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-1%29%2F%28x%5E2-5x%2B6%29%29%2B%28%28x%29%2F%28x-2%29%29=%28%282%29%2F%28x-3%29%29
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) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-1%29%2F%28x%5E2-5x%2B6%29%29%2B%28%28x%29%2F%28x-2%29%29=%28%282%29%2F%28x-3%29%29
I need steps and answer! Thanks!



**Note: x+%3C%3E+2, or x+%3C%3E+3, as these values would render the equation UNDEFINED

x - 1 + x(x - 3) = 2(x - 2) ------ Multiplying by LCD, x%5E2+-+5x+%2B+6, or (x - 2)(x - 3)

x+-+1+%2B+x%5E2+-+3x+=+2x+-+4

x%5E2+%2B+x+-+3x+-+2x+-+1+%2B+4+=+0

x%5E2+-+4x+%2B+3+=+0

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

x - 3 = 0 ------ x = 3 (ignore as it was stated before that: x+%3C%3E+3)

OR

x - 1 = 0 ----- highlight_green%28x+=+1%29

You can do the check!!

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