4-(3/(5+x))=2/(8+x)

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Solution for 4-(3/(5+x))=2/(8+x) equation: 


D( x )

x+5 = 0

x+8 = 0

x+5 = 0

x+5 = 0

x+5 = 0 // - 5

x = -5

x+8 = 0

x+8 = 0

x+8 = 0 // - 8

x = -8

x in (-oo:-8) U (-8:-5) U (-5:+oo)

4-(3/(x+5)) = 2/(x+8) // - 2/(x+8)

4-(3/(x+5))-(2/(x+8)) = 0

4-3*(x+5)^-1-2*(x+8)^-1 = 0

4-3/(x+5)-2/(x+8) = 0

(-3*(x+8))/((x+5)*(x+8))+(-2*(x+5))/((x+5)*(x+8))+(4*(x+5)*(x+8))/((x+5)*(x+8)) = 0

4*(x+5)*(x+8)-3*(x+8)-2*(x+5) = 0

4*x^2-5*x+52*x-34+160 = 0

4*x^2+47*x+126 = 0

4*x^2+47*x+126 = 0

4*x^2+47*x+126 = 0

DELTA = 47^2-(4*4*126)

DELTA = 193

DELTA > 0

x = (193^(1/2)-47)/(2*4) or x = (-193^(1/2)-47)/(2*4)

x = (193^(1/2)-47)/8 or x = (-(193^(1/2)+47))/8

(x+(193^(1/2)+47)/8)*(x-((193^(1/2)-47)/8)) = 0

((x+(193^(1/2)+47)/8)*(x-((193^(1/2)-47)/8)))/((x+5)*(x+8)) = 0

((x+(193^(1/2)+47)/8)*(x-((193^(1/2)-47)/8)))/((x+5)*(x+8)) = 0 // * (x+5)*(x+8)

(x+(193^(1/2)+47)/8)*(x-((193^(1/2)-47)/8)) = 0

( x+(193^(1/2)+47)/8 )

x+(193^(1/2)+47)/8 = 0 // - (193^(1/2)+47)/8

x = -((193^(1/2)+47)/8)

( x-((193^(1/2)-47)/8) )

x-((193^(1/2)-47)/8) = 0 // + (193^(1/2)-47)/8

x = (193^(1/2)-47)/8

x in { -((193^(1/2)+47)/8), (193^(1/2)-47)/8 }

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