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

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


D( x )

x^2-x-2 = 0

x+1 = 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 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

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

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

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

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

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

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

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

X^2-x^2 = 0

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

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

X^2-x^2 = 0

-1*x^2 = -X^2 // : -1

x^2 = X^2

x^2 = X^2 // ^ 1/2

abs(x) = X

x = X or x = -X

x in { X, -X }

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