N[Solve[2(x-((x^3)/(1-x)))-((1-3 x)/(1-x))(1+x-(x^2)+((x^3)/(1-x)))-(x^3)==0,x],10]

N[{(∂_x)( 2(x-((x^3)/(1-x)))-((1-3 x)/(1-x))(1+x-(x^2)+((x^3)/(1-x)))-(x^3))}/.{x->0.24240453395241098557732298786620182427`10.},5]

N[Solve[2(1+(x^2)-((x^3)/(1-x)))-((1-x)/x)(x+((x^3)/(1-x)))-(x^3)==0,x],10]

N[{(∂_x) (2(1+(x^2)-((x^3)/(1-x)))-((1-x)/x)(x+((x^3)/(1-x)))-(x^3))}/.{x->0.66963154669525743345143681493204082834`10.},5]

N[Solve[-((((5-4 x)(x^4))/(((x-1))^2))-4 (x^3)+1) (((x^5)/(1-x))+(x^3)+(x^2)+1)(((((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)-((((5-4 x)(x^4))/(((x-1))^2))-3 (x^2)-2 x+1) (((((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (((x^5)/(1-x))+(x^4)+x)+(((-((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)(-((x^5)/(1-x)) -(x^4)+x) (2 x+3 (x^2)-(((5-4 x)(x^4))/(((x-1))^2)))+(-((x^5)/(1-x))-(x^3)-(x^2)+x+1) (((-((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (-(((5-4 x)(x^4))/(((x-1))^2))+4 (x^3)+1)==0,x],10]

N[Solve[(∂_x) (-((((5-4 x)(x^4))/(((x-1))^2))-4 (x^3)+1) (((x^5)/(1-x))+(x^3)+(x^2)+1)(((((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)-((((5-4 x)(x^4))/(((x-1))^2))-3 (x^2)-2 x+1) (((((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (((x^5)/(1-x))+(x^4)+x)+(((-((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)(-((x^5)/(1-x)) -(x^4)+x) (2 x+3 (x^2)-(((5-4 x)(x^4))/(((x-1))^2)))+(-((x^5)/(1-x))-(x^3)-(x^2)+x+1) (((-((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (-(((5-4 x)(x^4))/(((x-1))^2))+4 (x^3)+1))==0,x],10]

N[{(∂_x) (-((((5-4 x)(x^4))/(((x-1))^2))-4 (x^3)+1) (((x^5)/(1-x))+(x^3)+(x^2)+1)(((((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)-((((5-4 x)(x^4))/(((x-1))^2))-3 (x^2)-2 x+1) (((((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (((x^5)/(1-x))+(x^4)+x)+(((-((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)(-((x^5)/(1-x)) -(x^4)+x) (2 x+3 (x^2)-(((5-4 x)(x^4))/(((x-1))^2)))+(-((x^5)/(1-x))-(x^3)-(x^2)+x+1) (((-((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (-(((5-4 x)(x^4))/(((x-1))^2))+4 (x^3)+1))}/.{x->1/4},5]

N[{-((((5-4 x)(x^4))/(((x-1))^2))-4 (x^3)+1) (((x^5)/(1-x))+(x^3)+(x^2)+1)(((((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)-((((5-4 x)(x^4))/(((x-1))^2))-3 (x^2)-2 x+1) (((((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (((x^5)/(1-x))+(x^4)+x)+(((-((x^5)/(1-x))-(x^3)-(x^2)+x+1))^2)(-((x^5)/(1-x)) -(x^4)+x) (2 x+3 (x^2)-(((5-4 x)(x^4))/(((x-1))^2)))+(-((x^5)/(1-x))-(x^3)-(x^2)+x+1) (((-((x^5)/(1-x))+(x^3)+(x^2)+1))^2) (-(((5-4 x)(x^4))/(((x-1))^2))+4 (x^3)+1)}/.{x->1/4}]

N[Solve[((x+(x^4)+((x^5)/(1-x)))/(1+x-(x^2)-(x^3)))-((x-(x^4)-((x^5)/(1-x)))/(1+(x^2)+(x^3)))==0,x],20]

N[{((x+(x^4)+((x^5)/(1-x)))/(1+x-(x^2)-(x^3)))-((x-(x^4)-((x^5)/(1-x)))/(1+(x^2)+(x^3)))}/.{x->0.286},10]

N[Solve[((x+(x^4)-((x^5)/(1-x)))/(1+x-(x^2)-(x^3)))-((x-(x^4)+((x^5)/(1-x)))/(1+(x^2)+(x^3)))==0,x],20]

N[{((x+(x^4)-((x^5)/(1-x)))/(1+x-(x^2)-(x^3)))-((x-(x^4)+((x^5)/(1-x)))/(1+(x^2)+(x^3)))}/.{x->0.329},10]