求解方程 50/(1+r) + 4/(hr)^2 + 2/(hr)^3 + 4/(1+r)^4 = 100 的详细步骤

我们可以先对等式两边的分式进行化简：\n\n50/(1+r) + 4/(hr)^2 + 2/(hr)^3 + 4/(1+r)^4 = 100\n\n将50/(1+r)化简为(50*(1+r))/(1+r) = 50，将4/(hr)^2化简为4/(h^2r^2)，将2/(hr)^3化简为2/(h^3r^3)，将4/(1+r)^4化简为4/(1+4r+6r^2+4r^3+r^4)。\n\n化简后的等式为：\n\n50 + 4/(h^2r^2) + 2/(h^3r^3) + 4/(1+4r+6r^2+4r^3+r^4) = 100\n\n将等式两边减去50，化简为：\n\n4/(h^2r^2) + 2/(h^3r^3) + 4/(1+4r+6r^2+4r^3+r^4) = 50\n\n移项得：\n\n4/(h^2r^2) + 2/(h^3r^3) = 50 - 4/(1+4r+6r^2+4r^3+r^4)\n\n化简右侧分式，得：\n\n4/(h^2r^2) + 2/(h^3r^3) = (50*(1+4r+6r^2+4r^3+r^4) - 4)/(1+4r+6r^2+4r^3+r^4)\n\n将左侧分式的通分，得：\n\n(4hr + 2)/(h^3r^3) = (50(1+4r+6r^2+4r^3+r^4) - 4)/(1+4r+6r^2+4r^3+r^4)\n\n将等式两边乘以h^3r^3，得：\n\n4hr + 2 = (50(1+4r+6r^2+4r^3+r^4) - 4)h^3r^3/(1+4r+6r^2+4r^3+r^4)\n\n继续化简右侧表达式，得：\n\n4hr + 2 = (50h^3r^3 + 200h^3r^4 + 300h^3r^5 + 200h^3r^6 + 50h^3r^7 - 4h^3r^3)/(1+4r+6r^2+4r^3+r^4)\n\n化简为：\n\n4hr + 2 = (200h^3r^4 + 300h^3r^5 + 200h^3r^6 + 50h^3r^7)/(1+4r+6r^2+4r^3+r^4)\n\n将等式两边减去2，得：\n\n4hr = (200h^3r^4 + 300h^3r^5 + 200h^3r^6 + 50h^3r^7)/(1+4r+6r^2+4r^3+r^4) - 2\n\n进一步化简右侧表达式，得：\n\n4hr = (200h^3r^4 + 300h^3r^5 + 200h^3r^6 + 50h^3r^7 - 2*(1+4r+6r^2+4r^3+r^4))/(1+4r+6r^2+4r^3+r^4)\n\n我们无法将右侧表达式进一步化简，因此无法得到r的具体解法。