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D( x )
2*x^2+5*x-3 = 0
x^2-9 = 0
(12*x+4)/(2*x^2+5*x-3) = 0
2*x^2+5*x-3 = 0
2*x^2+5*x-3 = 0
2*x^2+5*x-3 = 0
DELTA = 5^2-(-3*2*4)
DELTA = 49
DELTA > 0
x = (49^(1/2)-5)/(2*2) or x = (-49^(1/2)-5)/(2*2)
x = 1/2 or x = -3
x^2-9 = 0
x^2-9 = 0
1*x^2 = 9 // : 1
x^2 = 9
x^2 = 9 // ^ 1/2
abs(x) = 3
x = 3 or x = -3
(12*x+4)/(2*x^2+5*x-3) = 0
(12*x+4)/(2*x^2+5*x-3) = 0
2*x^2+5*x-3 = 0
2*x^2+5*x-3 = 0
DELTA = 5^2-(-3*2*4)
DELTA = 49
DELTA > 0
x = (49^(1/2)-5)/(2*2) or x = (-49^(1/2)-5)/(2*2)
x = 1/2 or x = -3
(x+3)*(x-1/2) = 0
(12*x+4)/((x+3)*(x-1/2)) = 0
12*x+4 = 0 // - 4
12*x = -4 // : 12
x = -4/12
x = -1/3
x in (-oo:-3) U (-3:-1/3) U (-1/3:1/2) U (1/2:3) U (3:+oo)
((2*x-6)/(x^2-9))/((12*x+4)/(2*x^2+5*x-3)) = 0
((2*x-6)*(2*x^2+5*x-3))/((x^2-9)*(12*x+4)) = 0
2*x^2+5*x-3 = 0
2*x^2+5*x-3 = 0
DELTA = 5^2-(-3*2*4)
DELTA = 49
DELTA > 0
x = (49^(1/2)-5)/(2*2) or x = (-49^(1/2)-5)/(2*2)
x = 1/2 or x = -3
(x+3)*(x-1/2) = 0
((2*x-6)*(x+3)*(x-1/2))/((x^2-9)*(12*x+4)) = 0
( 2*x-6 )
2*x-6 = 0 // + 6
2*x = 6 // : 2
x = 6/2
x = 3
( x+3 )
x+3 = 0 // - 3
x = -3
( x-1/2 )
x-1/2 = 0 // + 1/2
x = 1/2
x in { 3}
x in { -3}
x in { 1/2}
x belongs to the empty set
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