Question 1206450
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The given equation is equivalent to

    {{{((x-1)*(x+3))/(x+2)}}} = {{{2^2}}}

plus the condition that each factor in parentheses is positive number.


From it, we get

    (x-1)*(x+3) = 4*(x+2)

     x^2 - x + 3x - 3 = 4x + 8

     x^2 - 2x - 11 = 0


Apply the quadratic formula and find the roots

    {{{x{1,2]}}} = {{{(2 +- sqrt(2^2 - 4*1*(-11)))/2}}} = {{{(2 +- sqrt(48))/2}}} = {{{(2 +- 4*sqrt(3))/2}}} = {{{1 +- 2*sqrt(3)}}}.


One root is x = {{{1 + 2*sqrt(3)}}} = 4.4641  (rounded).


Another root is  {{{1-2*sqrt(3)}}} = -2.4641  (rounded).


Only positive root is the solution to the original equation, since (x-1) is also positive.


The negative root is not the solution to the original equation, since then (x-1) is negative, too.
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Solved, with explanations.