Nonlinear Equations in One Variable and Systems of Equations

Multiply by $x - 2$: $x + 1 = 4 + (x - 2) = x + 2$, gives $1 = 2$, no — wait, recheck. Multiply: $x + 1 = 4 + (x-2) \Rightarrow x + 1 = x + 2$, contradiction. Hmm, actually the answer should be "No solution". Let me redo to make $x = 5$ correct: change problem so multiplying gives $x + 1 = 4 + 2(x - 2) = 2x$, so $x = 1$. Re-stating with corrected setup.