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D( x )
x^2+1 = 0
x^2-6 = 0
x^2+1 = 0
x^2+1 = 0
1*x^2 = -1 // : 1
x^2 = -1
x^2-6 = 0
x^2-6 = 0
1*x^2 = 6 // : 1
x^2 = 6
x^2 = 6 // ^ 1/2
abs(x) = 6^(1/2)
x = 6^(1/2) or x = -6^(1/2)
x in (-oo:-6^(1/2)) U (-6^(1/2):6^(1/2)) U (6^(1/2):+oo)
(7*x^2+5*x)/(x^2+1)-((5*x)/(x^2-6)) = 0
(7*x^2+5*x)/(x^2+1)-5*x*(x^2-6)^-1 = 0
(7*x^2+5*x)/(x^2+1)+(-5*x)/(x^2-6) = 0
((7*x^2+5*x)*(x^2-6))/((x^2+1)*(x^2-6))+(-5*x*(x^2+1))/((x^2+1)*(x^2-6)) = 0
(7*x^2+5*x)*(x^2-6)-5*x*(x^2+1) = 0
7*x^4-42*x^2-35*x = 0
7*x^4-42*x^2-35*x = 0
7*x*(x^3-6*x-5) = 0
x^3-6*x-5 = 0
{ 1, -1, 5, -5 }
1
x = 1
x^3-6*x-5 = -10
1
-1
x = -1
x^3-6*x-5 = 0
-1
x+1
x^2-x-5
x^3-6*x-5
x+1
-x^3-x^2
-x^2-6*x-5
x^2+x
-5*x-5
5*x+5
0
x^2-x-5 = 0
DELTA = (-1)^2-(-5*1*4)
DELTA = 21
DELTA > 0
x = (21^(1/2)+1)/(1*2) or x = (1-21^(1/2))/(1*2)
x = (21^(1/2)+1)/2 or x = (1-21^(1/2))/2
x in { (1-21^(1/2))/2, (21^(1/2)+1)/2, -1}
7*x*(x-((1-21^(1/2))/2))*(x-((21^(1/2)+1)/2))*(x+1) = 0
(7*x*(x-((1-21^(1/2))/2))*(x-((21^(1/2)+1)/2))*(x+1))/((x^2+1)*(x^2-6)) = 0
(7*x*(x-((1-21^(1/2))/2))*(x-((21^(1/2)+1)/2))*(x+1))/((x^2+1)*(x^2-6)) = 0 // * (x^2+1)*(x^2-6)
7*x*(x-((1-21^(1/2))/2))*(x-((21^(1/2)+1)/2))*(x+1) = 0
( 7*x )
7*x = 0 // : 7
x = 0
( x+1 )
x+1 = 0 // - 1
x = -1
( x-((1-21^(1/2))/2) )
x-((1-21^(1/2))/2) = 0 // + (1-21^(1/2))/2
x = (1-21^(1/2))/2
( x-((21^(1/2)+1)/2) )
x-((21^(1/2)+1)/2) = 0 // + (21^(1/2)+1)/2
x = (21^(1/2)+1)/2
x in { 0, -1, (1-21^(1/2))/2, (21^(1/2)+1)/2 }
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