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D( x )
25-x^2 = 0
x^2-25 = 0
25-x^2 = 0
25-x^2 = 0
-1*x^2 = -25 // : -1
x^2 = 25
x^2 = 25 // ^ 1/2
abs(x) = 5
x = 5 or x = -5
x^2-25 = 0
x^2-25 = 0
1*x^2 = 25 // : 1
x^2 = 25
x^2 = 25 // ^ 1/2
abs(x) = 5
x = 5 or x = -5
x in (-oo:-5) U (-5:5) U (5:+oo)
(x-4)/(x^2-25)-((x-4)/(25-x^2)) = 0
(x-4)/(x^2-25)+(-1*(x-4))/(25-x^2) = 0
((x-4)*(25-x^2))/((x^2-25)*(25-x^2))+(-1*(x-4)*(x^2-25))/((x^2-25)*(25-x^2)) = 0
(x-4)*(25-x^2)-1*(x-4)*(x^2-25) = 0
8*x^2-2*x^3+50*x-200 = 0
8*x^2-2*x^3+50*x-200 = 0
2*(4*x^2-x^3+25*x-100) = 0
4*x^2-x^3+25*x-100 = 0
{ 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20, 25, -25, 50, -50, 100, -100 }
1
x = 1
4*x^2-x^3+25*x-100 = -72
1
-1
x = -1
4*x^2-x^3+25*x-100 = -120
-1
2
x = 2
4*x^2-x^3+25*x-100 = -42
2
-2
x = -2
4*x^2-x^3+25*x-100 = -126
-2
4
x = 4
4*x^2-x^3+25*x-100 = 0
4
x-4
25-x^2
4*x^2-x^3+25*x-100
x-4
x^3-4*x^2
25*x-100
100-25*x
0
25-x^2 = 0
DELTA = 0^2-(-1*4*25)
DELTA = 100
DELTA > 0
x = (100^(1/2)+0)/(-1*2) or x = (0-100^(1/2))/(-1*2)
x = -5 or x = 5
x in { -5, 5, 4}
2*(x+5)*(x-5)*(x-4) = 0
(2*(x+5)*(x-5)*(x-4))/((x^2-25)*(25-x^2)) = 0
(2*(x+5)*(x-5)*(x-4))/((x^2-25)*(25-x^2)) = 0 // * (x^2-25)*(25-x^2)
2*(x+5)*(x-5)*(x-4) = 0
( x+5 )
x+5 = 0 // - 5
x = -5
( x-4 )
x-4 = 0 // + 4
x = 4
( x-5 )
x-5 = 0 // + 5
x = 5
x in { -5}
x in { 5}
x = 4
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