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

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Solution for x/(x+2)(x-3)-2/(x-2)(x-3) equation:


D( x )

x-2 = 0

x+2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

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

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

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

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

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

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

x^3-7*x^2+8*x+12 = 0

x^3-7*x^2+8*x+12 = 0

x^3-7*x^2+8*x+12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

x^3-7*x^2+8*x+12 = 14

1

-1

x = -1

x^3-7*x^2+8*x+12 = -4

-1

2

x = 2

x^3-7*x^2+8*x+12 = 8

2

-2

x = -2

x^3-7*x^2+8*x+12 = -40

-2

3

x = 3

x^3-7*x^2+8*x+12 = 0

3

x-3

x^2-4*x-4

x^3-7*x^2+8*x+12

x-3

3*x^2-x^3

8*x-4*x^2+12

4*x^2-12*x

12-4*x

4*x-12

0

x^2-4*x-4 = 0

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

DELTA = 32

DELTA > 0

x = (32^(1/2)+4)/(1*2) or x = (4-32^(1/2))/(1*2)

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

x in { (4-4*2^(1/2))/2, (4*2^(1/2)+4)/2, 3}

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

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

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

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

( x-((4*2^(1/2)+4)/2) )

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

x = (4*2^(1/2)+4)/2

( x-((4-4*2^(1/2))/2) )

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

x = (4-4*2^(1/2))/2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { (4*2^(1/2)+4)/2, (4-4*2^(1/2))/2, 3 }

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