(x+3)/(x^2-2x)-10/(x^2-4)

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Solution for (x+3)/(x^2-2x)-10/(x^2-4) equation: 


D( x )

x^2-(2*x) = 0

x^2-4 = 0

x^2-(2*x) = 0

x^2-(2*x) = 0

x^2-2*x = 0

x^2-2*x = 0

DELTA = (-2)^2-(0*1*4)

DELTA = 4

DELTA > 0

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

x = 2 or x = 0

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:0) U (0:2) U (2:+oo)

(x+3)/(x^2-(2*x))-(10/(x^2-4)) = 0

(x+3)/(x^2-2*x)-10*(x^2-4)^-1 = 0

(x+3)/(x^2-2*x)-10/(x^2-4) = 0

x^2-2*x = 0

x^2-2*x = 0

x*(x-2) = 0

x-2 = 0 // + 2

x = 2

x*(x-2) = 0

(x+3)/(x*(x-2))-10/(x^2-4) = 0

((x+3)*(x^2-4))/(x*(x-2)*(x^2-4))+(-10*x*(x-2))/(x*(x-2)*(x^2-4)) = 0

(x+3)*(x^2-4)-10*x*(x-2) = 0

x^3-7*x^2+16*x-12 = 0

x^3-7*x^2+16*x-12 = 0

x^3-7*x^2+16*x-12 = 0

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

1

x = 1

x^3-7*x^2+16*x-12 = -2

1

-1

x = -1

x^3-7*x^2+16*x-12 = -36

-1

2

x = 2

x^3-7*x^2+16*x-12 = 0

2

x-2

x^2-5*x+6

x^3-7*x^2+16*x-12

x-2

2*x^2-x^3

16*x-5*x^2-12

5*x^2-10*x

6*x-12

12-6*x

0

x^2-5*x+6 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

x = (1^(1/2)+5)/(1*2) or x = (5-1^(1/2))/(1*2)

x = 3 or x = 2

x in { 2, 3, 2} 

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

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

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

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

( x-2 )

x-2 = 0 // + 2

x = 2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 2} 

x = 3

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