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D( x )
x-5 = 0
x+5 = 0
x^2-25 = 0
x-5 = 0
x-5 = 0
x-5 = 0 // + 5
x = 5
x+5 = 0
x+5 = 0
x+5 = 0 // - 5
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)
7/(x-5)+x/(x+5) = 42/(x^2-25) // - 42/(x^2-25)
7/(x-5)+x/(x+5)-(42/(x^2-25)) = 0
7/(x-5)+x/(x+5)-42*(x^2-25)^-1 = 0
7/(x-5)+x/(x+5)-42/(x^2-25) = 0
(7*(x+5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(x*(x-5)*(x^2-25))/((x-5)*(x+5)*(x^2-25))+(-42*(x-5)*(x+5))/((x-5)*(x+5)*(x^2-25)) = 0
7*(x+5)*(x^2-25)+x*(x-5)*(x^2-25)-42*(x-5)*(x+5) = 0
x^4+2*x^3+10*x^2-42*x^2-50*x-875+1050 = 0
x^4+2*x^3-32*x^2-50*x+175 = 0
x^4+2*x^3-32*x^2-50*x+175 = 0
x^4+2*x^3-32*x^2-50*x+175 = 0
{ 1, -1, 5, -5, 7, -7, 25, -25, 35, -35, 175, -175 }
1
x = 1
x^4+2*x^3-32*x^2-50*x+175 = 96
1
-1
x = -1
x^4+2*x^3-32*x^2-50*x+175 = 192
-1
5
x = 5
x^4+2*x^3-32*x^2-50*x+175 = 0
5
x-5
x^3+7*x^2+3*x-35
x^4+2*x^3-32*x^2-50*x+175
x-5
5*x^3-x^4
7*x^3-32*x^2-50*x+175
35*x^2-7*x^3
3*x^2-50*x+175
15*x-3*x^2
175-35*x
35*x-175
0
x^3+7*x^2+3*x-35 = 0
{ 1, -1, 5, -5, 7, -7, 35, -35 }
1
x = 1
x^3+7*x^2+3*x-35 = -24
1
-1
x = -1
x^3+7*x^2+3*x-35 = -32
-1
5
x = 5
x^3+7*x^2+3*x-35 = 280
5
-5
x = -5
x^3+7*x^2+3*x-35 = 0
-5
x+5
x^2+2*x-7
x^3+7*x^2+3*x-35
x+5
-x^3-5*x^2
2*x^2+3*x-35
-2*x^2-10*x
-7*x-35
7*x+35
0
x^2+2*x-7 = 0
DELTA = 2^2-(-7*1*4)
DELTA = 32
DELTA > 0
x = (32^(1/2)-2)/(1*2) or x = (-32^(1/2)-2)/(1*2)
x = (4*2^(1/2)-2)/2 or x = (-4*2^(1/2)-2)/2
x in { (-4*2^(1/2)-2)/2, (4*2^(1/2)-2)/2, 5, -5}
(x-((-4*2^(1/2)-2)/2))*(x-((4*2^(1/2)-2)/2))*(x-5)*(x+5) = 0
((x-((-4*2^(1/2)-2)/2))*(x-((4*2^(1/2)-2)/2))*(x-5)*(x+5))/((x-5)*(x+5)*(x^2-25)) = 0
((x-((-4*2^(1/2)-2)/2))*(x-((4*2^(1/2)-2)/2))*(x-5)*(x+5))/((x-5)*(x+5)*(x^2-25)) = 0 // * (x-5)*(x+5)*(x^2-25)
(x-((-4*2^(1/2)-2)/2))*(x-((4*2^(1/2)-2)/2))*(x-5)*(x+5) = 0
( x+5 )
x+5 = 0 // - 5
x = -5
( x-((-4*2^(1/2)-2)/2) )
x-((-4*2^(1/2)-2)/2) = 0 // + (-4*2^(1/2)-2)/2
x = (-4*2^(1/2)-2)/2
( x-((4*2^(1/2)-2)/2) )
x-((4*2^(1/2)-2)/2) = 0 // + (4*2^(1/2)-2)/2
x = (4*2^(1/2)-2)/2
( x-5 )
x-5 = 0 // + 5
x = 5
x in { -5}
x in { 5}
x in { (-4*2^(1/2)-2)/2, (4*2^(1/2)-2)/2 }
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