((5)/(2x+4)+4)=((-1)/(x+2))

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Solution for ((5)/(2x+4)+4)=((-1)/(x+2)) equation: 


D( x )

x+2 = 0

2*x+4 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

2*x+4 = 0

2*x+4 = 0

2*x+4 = 0 // - 4

2*x = -4 // : 2

x = -4/2

x = -2

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

5/(2*x+4)+4 = -1/(x+2) // + -1/(x+2)

5/(2*x+4)-(-1/(x+2))+4 = 0

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

5/(2*x+4)+1/(x+2)+4 = 0

(5*(x+2))/((2*x+4)*(x+2))+(2*x+4)/((2*x+4)*(x+2))+(4*(2*x+4)*(x+2))/((2*x+4)*(x+2)) = 0

5*(x+2)+4*(2*x+4)*(x+2)+2*x+4 = 0

8*x^2+7*x+32*x+14+32 = 0

8*x^2+39*x+46 = 0

8*x^2+39*x+46 = 0

8*x^2+39*x+46 = 0

DELTA = 39^2-(4*8*46)

DELTA = 49

DELTA > 0

x = (49^(1/2)-39)/(2*8) or x = (-49^(1/2)-39)/(2*8)

x = -2 or x = -23/8

(x+23/8)*(x+2) = 0

((x+23/8)*(x+2))/((2*x+4)*(x+2)) = 0

((x+23/8)*(x+2))/((2*x+4)*(x+2)) = 0 // * (2*x+4)*(x+2)

(x+23/8)*(x+2) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x+23/8 )

x+23/8 = 0 // - 23/8

x = -23/8

x in { -2} 

x = -23/8

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