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D( x )
x^2-x-6 = 0
x^2-x-6 = 0
x^2-x-6 = 0
x^2-x-6 = 0
DELTA = (-1)^2-(-6*1*4)
DELTA = 25
DELTA > 0
x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)
x = 3 or x = -2
x in (-oo:-2) U (-2:3) U (3:+oo)
(x^2-7)/(x^2-x-6) < 1 // - 1
(x^2-7)/(x^2-x-6)-1 < 0
x^2-x-6 < 0
x^2-x-6 = 0
x^2-x-6 = 0
DELTA = (-1)^2-(-6*1*4)
DELTA = 25
DELTA > 0
x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)
x = 3 or x = -2
(x+2)*(x-3) = 0
(x^2-7)/((x+2)*(x-3))-1 < 0
(x^2-7)/((x+2)*(x-3))+(-1*(x+2)*(x-3))/((x+2)*(x-3)) < 0
x^2-1*(x+2)*(x-3)-7 < 0
x-1 < 0
(x-1)/((x+2)*(x-3)) < 0
(x-1)/((x+2)*(x-3)) < 0 // * ((x+2)*(x-3))^2
(x-1)*(x+2)*(x-3) < 0
( x+2 )
x+2 < 0 // - 2
x < -2
( x-1 )
x-1 < 0 // + 1
x < 1
( x-3 )
x-3 < 0 // + 3
x < 3
(-oo:-2) (-2:1) (1:3) (3:+oo) x+2 - + + + x-1 - - + + x-3 - - - +
x in (-oo:-2) U (1:3)
(-oo:-2) U (1:3)
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