Question

Solve the nonlinear inequality (x^2 -2x +3) / (x+1) less than or equal to 1

Answer 1

$x\not=-1\\\\ \dfrac{x^2-2x+3}{x+1}\leq1\\ \dfrac{x^2-2x+3}{x+1}-1\leq0\\ \dfrac{x^2-2x+3}{x+1}-\dfrac{x+1}{x+1}\leq0\\ \dfrac{x^2-3x+2}{x+1}\leq0\\ (x^2-3x+2)(x+1)\leq0\\ (x^2-x-2x+2)(x+1)\leq0\\ (x(x-1)-2(x-1))(x+1)\leq0\\ (x-2)(x-1)(x+1)\leq0\\ \boxed{x\in (\infty,-1\rangle\cup(1,2\rangle}$