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

1 answer:

kondor19780726 [428]3 years ago

4 0

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

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