(-5/(4y+16))+1=(8/(y+4))

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Solution for (-5/(4y+16))+1=(8/(y+4)) equation: 


D( y )

4*y+16 = 0

y+4 = 0

4*y+16 = 0

4*y+16 = 0

4*y+16 = 0 // - 16

4*y = -16 // : 4

y = -16/4

y = -4

y+4 = 0

y+4 = 0

y+4 = 0 // - 4

y = -4

y in (-oo:-4) U (-4:+oo)

1-5/(4*y+16) = 8/(y+4) // - 8/(y+4)

1-5/(4*y+16)-(8/(y+4)) = 0

1-5/(4*y+16)-8*(y+4)^-1 = 0

1-5/(4*y+16)-8/(y+4) = 0

(-5*(y+4))/((4*y+16)*(y+4))+(-8*(4*y+16))/((4*y+16)*(y+4))+(1*(4*y+16)*(y+4))/((4*y+16)*(y+4)) = 0

1*(4*y+16)*(y+4)-5*(y+4)-8*(4*y+16) = 0

4*y^2-37*y+32*y-148+64 = 0

4*y^2-5*y-84 = 0

4*y^2-5*y-84 = 0

4*y^2-5*y-84 = 0

DELTA = (-5)^2-(-84*4*4)

DELTA = 1369

DELTA > 0

y = (1369^(1/2)+5)/(2*4) or y = (5-1369^(1/2))/(2*4)

y = 21/4 or y = -4

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

((y+4)*(y-21/4))/((4*y+16)*(y+4)) = 0

((y+4)*(y-21/4))/((4*y+16)*(y+4)) = 0 // * (4*y+16)*(y+4)

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

( y+4 )

y+4 = 0 // - 4

y = -4

( y-21/4 )

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

y = 21/4

y in { -4} 

y = 21/4

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