-(4/(y+2))=(5/(2y+4))+2

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Solution for -(4/(y+2))=(5/(2y+4))+2 equation: 


D( y )

y+2 = 0

2*y+4 = 0

y+2 = 0

y+2 = 0

y+2 = 0 // - 2

y = -2

2*y+4 = 0

2*y+4 = 0

2*y+4 = 0 // - 4

2*y = -4 // : 2

y = -4/2

y = -2

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

-(4/(y+2)) = 5/(2*y+4)+2 // - 5/(2*y+4)+2

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

-4*(y+2)^-1-5*(2*y+4)^-1-2 = 0

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

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

-4*(2*y+4)-5*(y+2)-2*(y+2)*(2*y+4) = 0

-4*y^2-13*y-16*y-26-16 = 0

-4*y^2-29*y-42 = 0

-4*y^2-29*y-42 = 0

-1*(4*y^2+29*y+42) = 0

4*y^2+29*y+42 = 0

DELTA = 29^2-(4*4*42)

DELTA = 169

DELTA > 0

y = (169^(1/2)-29)/(2*4) or y = (-169^(1/2)-29)/(2*4)

y = -2 or y = -21/4

-1*(y+21/4)*(y+2) = 0

(-1*(y+21/4)*(y+2))/((y+2)*(2*y+4)) = 0

(-1*(y+21/4)*(y+2))/((y+2)*(2*y+4)) = 0 // * (y+2)*(2*y+4)

-1*(y+21/4)*(y+2) = 0

( y+2 )

y+2 = 0 // - 2

y = -2

( y+21/4 )

y+21/4 = 0 // - 21/4

y = -21/4

y in { -2} 

y = -21/4

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