-6/(y+2)=2/(3y+6)-1

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Solution for -6/(y+2)=2/(3y+6)-1 equation: 


D( y )

y+2 = 0

3*y+6 = 0

y+2 = 0

y+2 = 0

y+2 = 0 // - 2

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:+oo)

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

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

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

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

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

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

3*y^2-20*y+12*y-40+12 = 0

3*y^2-8*y-28 = 0

3*y^2-8*y-28 = 0

3*y^2-8*y-28 = 0

DELTA = (-8)^2-(-28*3*4)

DELTA = 400

DELTA > 0

y = (400^(1/2)+8)/(2*3) or y = (8-400^(1/2))/(2*3)

y = 14/3 or y = -2

(y+2)*(y-14/3) = 0

((y+2)*(y-14/3))/((y+2)*(3*y+6)) = 0

((y+2)*(y-14/3))/((y+2)*(3*y+6)) = 0 // * (y+2)*(3*y+6)

(y+2)*(y-14/3) = 0

( y+2 )

y+2 = 0 // - 2

y = -2

( y-14/3 )

y-14/3 = 0 // + 14/3

y = 14/3

y in { -2} 

y = 14/3

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