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D( x )
x-3 = 0
x^2-(6*x)-7 = 0
x-3 = 0
x-3 = 0
x-3 = 0 // + 3
x = 3
x^2-(6*x)-7 = 0
x^2-(6*x)-7 = 0
x^2-6*x-7 = 0
x^2-6*x-7 = 0
DELTA = (-6)^2-(-7*1*4)
DELTA = 64
DELTA > 0
x = (64^(1/2)+6)/(1*2) or x = (6-64^(1/2))/(1*2)
x = 7 or x = -1
x in (-oo:-1) U (-1:3) U (3:7) U (7:+oo)
(2*x-5)/(x^2-(6*x)-7) < 1/(x-3) // - 1/(x-3)
(2*x-5)/(x^2-(6*x)-7)-(1/(x-3)) < 0
(2*x-5)/(x^2-6*x-7)-(x-3)^-1 < 0
(2*x-5)/(x^2-6*x-7)-1/(x-3) < 0
x^2-6*x-7 < 0
x^2-6*x-7 = 0
x^2-6*x-7 = 0
DELTA = (-6)^2-(-7*1*4)
DELTA = 64
DELTA > 0
x = (64^(1/2)+6)/(1*2) or x = (6-64^(1/2))/(1*2)
x = 7 or x = -1
(x+1)*(x-7) = 0
(2*x-5)/((x+1)*(x-7))-1/(x-3) < 0
((2*x-5)*(x-3))/((x+1)*(x-7)*(x-3))+(-1*(x+1)*(x-7))/((x+1)*(x-7)*(x-3)) < 0
(2*x-5)*(x-3)-1*(x+1)*(x-7) < 0
x^2-5*x+22 < 0
x^2-5*x+22 = 0
x^2-5*x+22 = 0
DELTA = (-5)^2-(1*4*22)
DELTA = -63
DELTA < 0
1 = 0
1/((x+1)*(x-7)*(x-3)) < 0
1/((x+1)*(x-7)*(x-3)) < 0 // * ((x+1)*(x-7)*(x-3))^2
(x+1)*(x-7)*(x-3) < 0
( x+1 )
x+1 < 0 // - 1
x < -1
( x-3 )
x-3 < 0 // + 3
x < 3
( x-7 )
x-7 < 0 // + 7
x < 7
(-oo:-1) (-1:3) (3:7) (7:+oo) x+1 - + + + x-3 - - + + x-7 - - - +
x in (-oo:-1) U (3:7)
(-oo:-1) U (3:7)
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