Question

|x^2-1|:(x-1)=4

Answer 1

\(\dfrac{x^2-1}{x-1}=4\left(x\ne1\right)\)

\(\Leftrightarrow\dfrac{x^2-1}{x-1}-4=0\)

\(\Leftrightarrow x^2-1-4\left(x-1\right)=0\)

\(\Leftrightarrow x^2-1-4x+4=0\)

\(\Leftrightarrow x^2-4x+3=0\)

\(\Leftrightarrow\left(x-3\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\left(n\right)\\x=1\left(l\right)\end{matrix}\right.\)

\(S=\left\{3\right\}\)

Answer 2

        |x² - 1| : (x -1) = 4

<=>  |x² - 1| = 4. (x -1)

<=> |x² - 1| = 4x -4

TH1: x² - 1 \(\ge\) 0 <=> x² \(\ge1\) 

      x² - 1 = 4x -4

<=> x² -  4x + 3 = 0

<=> x = 3 hoặc x = 1 (tm)

TH1: x² - 1 \(\le\) 0 <=> x² \(\le1\) 

1 - x²  = 4x -4

<=> - x²  - 4x + 5 = 0

<=> x = 1 hoặc x = -5 (tm)