x/(x^2+x-12)=2/(x-3)-5/(x+4)

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Solution for x/(x^2+x-12)=2/(x-3)-5/(x+4) equation: 


D( x )

x+4 = 0

x^2+x-12 = 0

x-3 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x^2+x-12 = 0

x^2+x-12 = 0

x^2+x-12 = 0

DELTA = 1^2-(-12*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-1)/(1*2) or x = (-49^(1/2)-1)/(1*2)

x = 3 or x = -4

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:-4) U (-4:3) U (3:+oo)

x/(x^2+x-12) = 2/(x-3)-(5/(x+4)) // - 2/(x-3)-(5/(x+4))

x/(x^2+x-12)-(2/(x-3))+5/(x+4) = 0

x/(x^2+x-12)-2*(x-3)^-1+5/(x+4) = 0

x/(x^2+x-12)-2/(x-3)+5/(x+4) = 0

x^2+x-12 = 0

x^2+x-12 = 0

x^2+x-12 = 0

DELTA = 1^2-(-12*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-1)/(1*2) or x = (-49^(1/2)-1)/(1*2)

x = 3 or x = -4

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

x/((x+4)*(x-3))-2/(x-3)+5/(x+4) = 0

x/((x+4)*(x-3))+(-2*(x+4))/((x+4)*(x-3))+(5*(x-3))/((x+4)*(x-3)) = 0

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

5*x-x-15-8 = 0

4*x-23 = 0

(4*x-23)/((x+4)*(x-3)) = 0

(4*x-23)/((x+4)*(x-3)) = 0 // * (x+4)*(x-3)

4*x-23 = 0

4*x-23 = 0 // + 23

4*x = 23 // : 4

x = 23/4

x = 23/4

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