Question 692957

Could a friendly soul please assist with this problem: Bless your heart. I need to understand work process and how answer was gotten. Thankyou.

Solve:  1/x-1 + 2/x  =  x/x-1

Rational Equation


{{{1/(x - 1) + 2/x = x/(x - 1)}}}


** Note that {{{x <> 1}}}, or {{{x <> 0}}}, since these values would render fractions in the equation as UNDEFINED.


{{{x + 2(x - 1) = x^2}}} ------ Multiplying by LCD, x(x - 1)


{{{x + 2x - 2 = x^2}}}


{{{3x - 2 = x^2}}}


{{{x^2 - 3x + 2 = 0}}}


(x - 1)(x - 2) = 0


x = 1 = 0, or x = 1


As explained above, {{{x <> 1}}}, so 


x - 2 = 0, or {{{highlight_green(x = 2)}}}


You can do the check!!


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