3/(y^2-4)=-2/(3y+6)

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Solution for 3/(y^2-4)=-2/(3y+6) equation: 


D( y )

y^2-4 = 0

3*y+6 = 0

y^2-4 = 0

y^2-4 = 0

1*y^2 = 4 // : 1

y^2 = 4

y^2 = 4 // ^ 1/2

abs(y) = 2

y = 2 or y = -2

3*y+6 = 0

3*y+6 = 0

3*y+6 = 0 // - 6

3*y = -6 // : 3

y = -6/3

y = -2

y in (-oo:-2) U (-2:2) U (2:+oo)

3/(y^2-4) = -2/(3*y+6) // + -2/(3*y+6)

3/(y^2-4)-(-2/(3*y+6)) = 0

3/(y^2-4)+2*(3*y+6)^-1 = 0

3/(y^2-4)+2/(3*y+6) = 0

(3*(3*y+6))/((y^2-4)*(3*y+6))+(2*(y^2-4))/((y^2-4)*(3*y+6)) = 0

3*(3*y+6)+2*(y^2-4) = 0

2*y^2+9*y+10 = 0

2*y^2+9*y+10 = 0

2*y^2+9*y+10 = 0

DELTA = 9^2-(2*4*10)

DELTA = 1

DELTA > 0

y = (1^(1/2)-9)/(2*2) or y = (-1^(1/2)-9)/(2*2)

y = -2 or y = -5/2

(y+5/2)*(y+2) = 0

((y+5/2)*(y+2))/((y^2-4)*(3*y+6)) = 0

((y+5/2)*(y+2))/((y^2-4)*(3*y+6)) = 0 // * (y^2-4)*(3*y+6)

(y+5/2)*(y+2) = 0

( y+2 )

y+2 = 0 // - 2

y = -2

( y+5/2 )

y+5/2 = 0 // - 5/2

y = -5/2

y in { -2} 

y = -5/2

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