\(=\lim\limits_{x\rightarrow1}\dfrac{\left(x+1-1\right)\left(\sqrt[4]{\left(2x+1\right)^3}+\sqrt[4]{\left(2x+1\right)^2}+\sqrt[4]{2x+1}+1\right)}{\left(2x+1-1\right)\left(\sqrt[3]{\left(x+1\right)^2}+\sqrt[3]{x+1}+1\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{\sqrt[4]{\left(2x+1\right)^3}+\sqrt[4]{\left(2x+1\right)^2}+\sqrt[4]{2x+1}+1}{2\left(\sqrt[3]{\left(x+1\right)^2}+\sqrt[3]{x+1}+1\right)}\)
\(=\dfrac{\sqrt[4]{\left(2+1\right)^3}+\sqrt[4]{\left(2+1\right)^2}+\sqrt[4]{2+1}+1}{2.\left(\sqrt[3]{\left(1+1\right)^2}+\sqrt[3]{1+1}+1\right)}=....\)