(14/(x+3))+(10/(x-2))=(122/(x^2+x-6))

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Solution for (14/(x+3))+(10/(x-2))=(122/(x^2+x-6)) equation: 


D( x )

x-2 = 0

x+3 = 0

x^2+x-6 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x+3 = 0

x+3 = 0

x+3 = 0 // - 3

x = -3

x^2+x-6 = 0

x^2+x-6 = 0

x^2+x-6 = 0

DELTA = 1^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

x in (-oo:-3) U (-3:2) U (2:+oo)

14/(x+3)+10/(x-2) = 122/(x^2+x-6) // - 122/(x^2+x-6)

14/(x+3)+10/(x-2)-(122/(x^2+x-6)) = 0

14/(x+3)+10/(x-2)-122*(x^2+x-6)^-1 = 0

14/(x+3)+10/(x-2)-122/(x^2+x-6) = 0

x^2+x-6 = 0

x^2+x-6 = 0

x^2+x-6 = 0

DELTA = 1^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-1)/(1*2) or x = (-25^(1/2)-1)/(1*2)

x = 2 or x = -3

(x+3)*(x-2) = 0

14/(x+3)+10/(x-2)-122/((x+3)*(x-2)) = 0

(14*(x-2))/((x+3)*(x-2))+(10*(x+3))/((x+3)*(x-2))-122/((x+3)*(x-2)) = 0

14*(x-2)+10*(x+3)-122 = 0

24*x-122+2 = 0

24*x-120 = 0

(24*x-120)/((x+3)*(x-2)) = 0

(24*x-120)/((x+3)*(x-2)) = 0 // * (x+3)*(x-2)

24*x-120 = 0

24*x-120 = 0 // + 120

24*x = 120 // : 24

x = 120/24

x = 5

x = 5

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