x/2x-3+4/(x+1)=1

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Solution for x/2x-3+4/(x+1)=1 equation: 


D( x )

x+1 = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-1) U (-1:+oo)

4/(x+1)+(x/2)*x-3 = 1 // - 1

4/(x+1)+(x/2)*x-3-1 = 0

4/(x+1)+(x^2)/2-3-1 = 0

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

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

x^3+x^2-6*x-2*x-6-2+8 = 0

x^3+x^2-6*x-2*x-2+2 = 0

x^3+x^2-8*x = 0

x^3+x^2-8*x = 0

x*(x^2+x-8) = 0

x^2+x-8 = 0

DELTA = 1^2-(-8*1*4)

DELTA = 33

DELTA > 0

x = (33^(1/2)-1)/(1*2) or x = (-33^(1/2)-1)/(1*2)

x = (33^(1/2)-1)/2 or x = (-(33^(1/2)+1))/2

x*(x+(33^(1/2)+1)/2)*(x-((33^(1/2)-1)/2)) = 0

(x*(x+(33^(1/2)+1)/2)*(x-((33^(1/2)-1)/2)))/(2*(x+1)) = 0

(x*(x+(33^(1/2)+1)/2)*(x-((33^(1/2)-1)/2)))/(2*(x+1)) = 0 // * 2*(x+1)

x*(x+(33^(1/2)+1)/2)*(x-((33^(1/2)-1)/2)) = 0

( x+(33^(1/2)+1)/2 )

x+(33^(1/2)+1)/2 = 0 // - (33^(1/2)+1)/2

x = -((33^(1/2)+1)/2)

( x-((33^(1/2)-1)/2) )

x-((33^(1/2)-1)/2) = 0 // + (33^(1/2)-1)/2

x = (33^(1/2)-1)/2

( x )

x = 0

x in { -((33^(1/2)+1)/2), (33^(1/2)-1)/2, 0 }

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