Question

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

Answer 1

`x\\ot=-1\\\\ (x^2-2x+3)/(x+1)\leq1\\ (x^2-2x+3)/(x+1)-1\leq0\\ (x^2-2x+3)/(x+1)-(x+1)/(x+1)\leq0\\ (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}`