Question 696652

What is the solution set of the equation (x/x-4)-(1/x+3)=(28/x^2-x-12)?

Please help and thank you! I really appreciate it. 


{{{x/(x - 4) - 1/(x + 3) = 28/(x^2 - x - 12)}}}


** Note that for this equation, {{{x <> 4}}}, and {{{x <> - 3}}}


x(x + 3) - 1(x - 4) = 28 ----- Multiplying by LCD, (x - 4)(x + 3), or {{{x^2 - x - 12}}}


{{{x^2 + 3x - x + 4 = 28}}}


{{{x^2 + 2x + 4 - 28 = 0)))


{{{x^2 + 2x - 24 = 0}}}


(x + 6)(x - 4) = 0


x + 6 = 0 ----- {{{highlight(x = - 6)}}}


x - 4 = 0 ---- {{{highlight(x = 4)}}}. However, as stated previously, {{{x <> 4}}}.


Therefore, only solution is: {{{highlight_green(x = - 6)}}}


You can do the check!!


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