(3/(x-2))+(4/(x+3))=(7/(x^2+x-6))

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Solution for (3/(x-2))+(4/(x+3))=(7/(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)

3/(x-2)+4/(x+3) = 7/(x^2+x-6) // - 7/(x^2+x-6)

3/(x-2)+4/(x+3)-(7/(x^2+x-6)) = 0

3/(x-2)+4/(x+3)-7*(x^2+x-6)^-1 = 0

3/(x-2)+4/(x+3)-7/(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

3/(x-2)+4/(x+3)-7/((x+3)*(x-2)) = 0

(3*(x+3))/((x-2)*(x+3))+(4*(x-2))/((x-2)*(x+3))-7/((x-2)*(x+3)) = 0

3*(x+3)+4*(x-2)-7 = 0

7*x-7+1 = 0

7*x-6 = 0

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

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

7*x-6 = 0

7*x-6 = 0 // + 6

7*x = 6 // : 7

x = 6/7

x = 6/7

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