(2/(x-3))+(3/(x+2))=(4/(x^2-x-6))

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Solution for (2/(x-3))+(3/(x+2))=(4/(x^2-x-6)) equation: 


D( x )

x^2-x-6 = 0

x+2 = 0

x-3 = 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 = (1-25^(1/2))/(1*2)

x = 3 or x = -2

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

2/(x-3)+3/(x+2) = 4/(x^2-x-6) // - 4/(x^2-x-6)

2/(x-3)+3/(x+2)-(4/(x^2-x-6)) = 0

2/(x-3)+3/(x+2)-4*(x^2-x-6)^-1 = 0

2/(x-3)+3/(x+2)-4/(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 = (1-25^(1/2))/(1*2)

x = 3 or x = -2

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

2/(x-3)+3/(x+2)-4/((x+2)*(x-3)) = 0

(2*(x+2))/((x-3)*(x+2))+(3*(x-3))/((x-3)*(x+2))-4/((x-3)*(x+2)) = 0

2*(x+2)+3*(x-3)-4 = 0

5*x-5-4 = 0

5*x-9 = 0

(5*x-9)/((x-3)*(x+2)) = 0

(5*x-9)/((x-3)*(x+2)) = 0 // * (x-3)*(x+2)

5*x-9 = 0

5*x-9 = 0 // + 9

5*x = 9 // : 5

x = 9/5

x = 9/5

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