\(M=\dfrac{x-1}{\sqrt[3]{x^2}-1}-\dfrac{\sqrt[3]{x}+2}{\sqrt[3]{x}+1}\)
\(M=\dfrac{x-1-\left(\sqrt[3]{x}+2\right)\left(\sqrt[3]{x}-1\right)}{\left(\sqrt[3]{x}+1\right)\left(\sqrt[3]{x}-1\right)}\)
\(M=\dfrac{x-\sqrt[3]{x^2}-\sqrt[3]{x}+1}{\left(\sqrt[3]{x}+1\right)\left(\sqrt[3]{x}-1\right)}\)
\(M=\dfrac{\left(\sqrt[3]{x}-1\right)^2\left(\sqrt[3]{x}+1\right)}{\left(\sqrt[3]{x}+1\right)\left(\sqrt[3]{x}-1\right)}\)
\(M=\sqrt[3]{x}-1\)