(2/(x+1))-(5/(x-2))=(x^2-6x-13)/(x^2-x-2)

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Solution for (2/(x+1))-(5/(x-2))=(x^2-6x-13)/(x^2-x-2) equation: 


D( x )

x-2 = 0

x^2-x-2 = 0

x+1 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x^2-x-2 = 0

x^2-x-2 = 0

x^2-x-2 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)+1)/(1*2) or x = (1-9^(1/2))/(1*2)

x = 2 or x = -1

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-1) U (-1:2) U (2:+oo)

2/(x+1)-(5/(x-2)) = (x^2-(6*x)-13)/(x^2-x-2) // - (x^2-(6*x)-13)/(x^2-x-2)

2/(x+1)-(5/(x-2))-((x^2-(6*x)-13)/(x^2-x-2)) = 0

2/(x+1)-5*(x-2)^-1-((x^2-6*x-13)/(x^2-x-2)) = 0

2/(x+1)-5/(x-2)+(-1*(x^2-6*x-13))/(x^2-x-2) = 0

x^2-x-2 = 0

x^2-x-2 = 0

x^2-x-2 = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)+1)/(1*2) or x = (1-9^(1/2))/(1*2)

x = 2 or x = -1

(x+1)*(x-2) = 0

2/(x+1)-5/(x-2)+(-1*(x^2-6*x-13))/((x+1)*(x-2)) = 0

(2*(x-2))/((x+1)*(x-2))+(-5*(x+1))/((x+1)*(x-2))+(-1*(x^2-6*x-13))/((x+1)*(x-2)) = 0

2*(x-2)-5*(x+1)-1*(x^2-6*x-13) = 0

6*x-x^2-3*x-9+13 = 0

3*x-x^2+4 = 0

3*x-x^2+4 = 0

3*x-x^2+4 = 0

DELTA = 3^2-(-1*4*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)-3)/(-1*2) or x = (-25^(1/2)-3)/(-1*2)

x = -1 or x = 4

(x+1)*(x-4) = 0

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

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

(x+1)*(x-4) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -1} 

x = 4

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