((7x^2+5x)/(x^2+1))-((5x)/(x^2-6))

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Solution for ((7x^2+5x)/(x^2+1))-((5x)/(x^2-6)) equation: 


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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