(2x/(x+4))+(8/x)=(32/((x^2)+4x))

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Solution for (2x/(x+4))+(8/x)=(32/((x^2)+4x)) equation: 


D( x )

x+4 = 0

x = 0

x^2+4*x = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x = 0

x = 0

x^2+4*x = 0

x^2+4*x = 0

x^2+4*x = 0

DELTA = 4^2-(0*1*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)-4)/(1*2) or x = (-16^(1/2)-4)/(1*2)

x = 0 or x = -4

x in (-oo:-4) U (-4:0) U (0:+oo)

(2*x)/(x+4)+8/x = 32/(x^2+4*x) // - 32/(x^2+4*x)

(2*x)/(x+4)-(32/(x^2+4*x))+8/x = 0

(2*x)/(x+4)-32*(x^2+4*x)^-1+8/x = 0

(2*x)/(x+4)-32/(x^2+4*x)+8/x = 0

x^2+4*x = 0

x^2+4*x = 0

x*(x+4) = 0

x+4 = 0 // - 4

x = -4

x*(x+4) = 0

(2*x)/(x+4)-32/(x*(x+4))+8/x = 0

(2*x*x)/(x*(x+4))-32/(x*(x+4))+(8*(x+4))/(x*(x+4)) = 0

8*(x+4)+2*x*x-32 = 0

2*x^2+8*x-32+32 = 0

2*x^2+8*x = 0

2*x^2+8*x = 0

2*x*(x+4) = 0

x+4 = 0 // - 4

x = -4

2*x*(x+4) = 0

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

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

2*x*(x+4) = 0

( 2*x )

2*x = 0 // : 2

x = 0

( x+4 )

x+4 = 0 // - 4

x = -4

x in { 0} 

x in { -4} 

x belongs to the empty set

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