6/(x+3)-5/(x-2)=-20/(x^2+x-6)

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Solution for 6/(x+3)-5/(x-2)=-20/(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)

6/(x+3)-(5/(x-2)) = -20/(x^2+x-6) // + -20/(x^2+x-6)

6/(x+3)-(5/(x-2))-(-20/(x^2+x-6)) = 0

6/(x+3)-5*(x-2)^-1+20*(x^2+x-6)^-1 = 0

6/(x+3)-5/(x-2)+20/(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

6/(x+3)-5/(x-2)+20/((x+3)*(x-2)) = 0

(6*(x-2))/((x+3)*(x-2))+(-5*(x+3))/((x+3)*(x-2))+20/((x+3)*(x-2)) = 0

6*(x-2)-5*(x+3)+20 = 0

x-27+20 = 0

x-7 = 0

(x-7)/((x+3)*(x-2)) = 0

(x-7)/((x+3)*(x-2)) = 0 // * (x+3)*(x-2)

x-7 = 0

x-7 = 0 // + 7

x = 7

x = 7

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