Solving a Quadratic InequalitySolve the inequality: x − 1 x 2 − 4 x + 3 &lt; 1.I cancelled the x − 1 from the numerator and the denominator and I obtained: x − 4 x − 3 .Thus, the answer that I got was x ∈ ( 3 , 4 ) .But according to WolframAlpha answer should be x ∈ ( 4 , ∞ ) ∪ ( 1 , 3 ) ∪ ( − ∞ , 1 ) .What is the best method to solve this inequality and where have I gone wrong?

Question

Solving a Quadratic InequalitySolve the inequality:                    x        −        1                              x          2                −        4        x        +        3              &amp;lt;  1.I cancelled the   x  −  1 from the numerator and the denominator and I obtained:            x      −      4              x      −      3        .Thus, the answer that I got was  x  ∈  (  3  ,  4  )  .But according to WolframAlpha answer should be  x  ∈  (  4  ,  ∞  )  ∪  (  1  ,  3  )  ∪  (  −  ∞  ,  1  )  .What is the best method to solve this inequality and where have I gone wrong?

Penelope Powers · Accepted Answer

It&#039;s      1          x      −      3        &amp;lt;  1and   x  ≠  1 or  1  −      1          x      −      3        &amp;gt;  0or            x      −      4              x      −      3        &amp;gt;  0  ,which by the intervals method gives   x  &amp;lt;  3 or   x  &amp;gt;  4 and with   x  ≠  1 we got the answer:  (  −  ∞  ,  1  )  ∪  (  1  ,  3  )  ∪  (  4  ,  +  ∞  )

Solving a Quadratic Inequality Solve the inequality: (x-1)/(x^2-4x+3)<1.

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