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

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Solution for (3/x^2-1)/(6/(7x^2+7x)) equation: 


D( x )

7*x^2+7*x = 0

x^2 = 0

6/(7*x^2+7*x) = 0

7*x^2+7*x = 0

7*x^2+7*x = 0

7*x^2+7*x = 0

DELTA = 7^2-(0*4*7)

DELTA = 49

DELTA > 0

x = (49^(1/2)-7)/(2*7) or x = (-49^(1/2)-7)/(2*7)

x = 0 or x = -1

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

6/(7*x^2+7*x) = 0

6/(7*x^2+7*x) = 0

7*x^2+7*x = 0

7*x*(x+1) = 0

x+1 = 0 // - 1

x = -1

7*x*(x+1) = 0

6/(7*x*(x+1)) = 0

x in (-oo:-1) U (-1:0) U (0:+oo)

(3/(x^2)-1)/(6/(7*x^2+7*x)) = 0

((3*x^-2-1)*(7*x^2+7*x))/6 = 0

7*x^2+7*x = 0

7*x*(x+1) = 0

x+1 = 0 // - 1

x = -1

7*x*(x+1) = 0

(7*x*(3*x^-2-1)*(x+1))/6 = 0

( 3*x^-2-1 )

3*x^-2 = 1 // : 3

x^-2 = 1/3

-2 < 0

1/(x^2) = 1/3 // * x^2

1 = 1/3*x^2 // : 1/3

3 = x^2

x^2 = 3 // ^ 1/2

abs(x) = 3^(1/2)

x = 3^(1/2) or x = -3^(1/2)

( 7*x )

7*x = 0 // : 7

x = 0

( x+1 )

x+1 = 0 // - 1

x = -1

x in { 0} 

x in { -1} 

x in { 3^(1/2), -3^(1/2) }

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