(2x^2)/(x^2+x-12)-(x-1)/(x-4)=(x+6)/(x-3)

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Solution for (2x^2)/(x^2+x-12)-(x-1)/(x-4)=(x+6)/(x-3) equation: 


D( x )

x^2+x-12 = 0

x-3 = 0

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-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

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

(2*x^2)/(x^2+x-12)-((x-1)/(x-4)) = (x+6)/(x-3) // - (x+6)/(x-3)

(2*x^2)/(x^2+x-12)-((x-1)/(x-4))-((x+6)/(x-3)) = 0

(2*x^2)/(x^2+x-12)+(-1*(x-1))/(x-4)+(-1*(x+6))/(x-3) = 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

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

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

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

x^3-x^3-8*x^2-6*x^2+13*x+16*x-12+96 = 0

29*x-14*x^2+84 = 0

29*x-14*x^2+84 = 0

29*x-14*x^2+84 = 0

DELTA = 29^2-(-14*4*84)

DELTA = 5545

DELTA > 0

x = (5545^(1/2)-29)/(-14*2) or x = (-5545^(1/2)-29)/(-14*2)

x = (5545^(1/2)-29)/(-28) or x = (5545^(1/2)+29)/28

(x-((5545^(1/2)-29)/(-28)))*(x-((5545^(1/2)+29)/28)) = 0

((x-((5545^(1/2)-29)/(-28)))*(x-((5545^(1/2)+29)/28)))/((x+4)*(x-3)*(x-4)) = 0

((x-((5545^(1/2)-29)/(-28)))*(x-((5545^(1/2)+29)/28)))/((x+4)*(x-3)*(x-4)) = 0 // * (x+4)*(x-3)*(x-4)

(x-((5545^(1/2)-29)/(-28)))*(x-((5545^(1/2)+29)/28)) = 0

( x-((5545^(1/2)+29)/28) )

x-((5545^(1/2)+29)/28) = 0 // + (5545^(1/2)+29)/28

x = (5545^(1/2)+29)/28

( x-((5545^(1/2)-29)/(-28)) )

x-((5545^(1/2)-29)/(-28)) = 0 // + (5545^(1/2)-29)/(-28)

x = (5545^(1/2)-29)/(-28)

x in { (5545^(1/2)+29)/28, (5545^(1/2)-29)/(-28) }

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