Karel solved the equation $$ (x+1)\cdot (2x-5) = (x+1)\cdot (x-1) $$ as follows:
(1) He divided both sides of the equation by the expression $(x+1)$ to simplify the equation: $$ 2x-5=x-1 $$
(2) He added $5$ to both sides of the equation and got: $$ 2x=x+4 $$
(3) He subtracted $x$ from both sides of the equation and obtained: $$ x=4 $$
Did Karel make an error anywhere? If yes, specify where.
Yes, the error is in step (1). When dividing both sides of the equation by $(x+1)$ he has not taken into account that this expression can take the value $0$. In this way he lost one solution, namely $x=-1$.
Yes, the error is in step (2). Moving $-5$ to the right side of the equation he should have got an equation $2x=x-6$.
Yes, the error is in step (3). The solution to the equation is $x=2$.
No, the solution is correct. We can confirm this by the following check: $$\begin{aligned} L&=(4+1)\cdot (2\cdot 4-5)=15\cr P&=(4+1) \cdot (4-1)=15 \end{aligned}$$