K.<p,d,e,g,m,f,h,l,r,N> = FractionField(PolynomialRing(QQ,10,'pdegmfhlrN'))
R.<s> = K[]
x = s + h/(4*l)
G = e*l*x^4 - e*h*x^3 + (-3*e*l-e*r+N)*x^2 + 2*e*h*s + 2*e*l + 2*e*r-N
print G

The response looks fishy: 

e*l*s^4 + ((-30423614405477505635920876929024*e*h^2 - 
243388915243820045087367015432192*e*l^2 - 
81129638414606681695789005144064*e*l*r + 
81129638414606681695789005144064*l*N)/(81129638414606681695789005144064*l))*s^2 
+ ((-2417851639229258349412352*e*h^3 + 9671406556917033397649408*e*h*l^2 - 
9671406556917033397649408*e*h*l*r + 
9671406556917033397649408*h*l*N)/(19342813113834066795298816*l^2))*s + 
(-3072*e*h^4 - 49152*e*h^2*l^2 + 524288*e*l^4 - 16384*e*h^2*l*r + 
524288*e*l^3*r + 16384*h^2*l*N - 262144*l^3*N)/(262144*l^3)

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