New posts in Module Isomorphism

Are two submodules (where one is contained in the other) isomorphic if their quotientmodules are isomorphic?

Showing that $\frac{\mathbb{R}[x]}{\langle x \rangle}$ and $\frac{\mathbb{R}[x]}{\langle x-1 \rangle}$ are not isomorphic as $\mathbb{R}[x]$ modules.