Question: Solve for x and check for extraneous solutions:

\[\frac{\mathrm{3}}{\mathrm{x}+\mathrm{1}}-\frac{\mathrm{x}-\mathrm{2}}{\mathrm{2}}=\frac{\mathrm{x}-\mathrm{2}}{\mathrm{x}+\mathrm{1}}\]