I have the following inequality:
$\frac{2x-3}{x+1}\leq1$
so, considering $x \neq -1$, I started multiplying $x+1$ both sides:
$2x-3\leq x+1$
then I subtracted $x$ both sides:
$x-3\leq1$
and then sum $3$ both sides:
$x\leq4$
Therefore, my solution for $x\neq-1$ is:
$(-\infty,4]$
But the book solution is:
$(-1,4]$
What I did wrong?