Question : Simplify:
${\frac{x^4-2 x^2+1}{x^2-2 x+1}}$
Option 1: $x^2-2 x+1$
Option 2: $x^2+2 x+2$
Option 3: $x^2+2 x+1$
Option 4: $x^2+x+1$
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Answer (1)
24th Jan, 2024
Correct Answer: $x^2+2 x+1$
Solution :
${\frac{x^4-2 x^2+1}{x^2-2 x+1}}$ .
$= \frac{(x^2-1)^2}{(x-1)^2}$
$=\frac{(x+1)^2(x-1)^2}{(x-1)^2}$
$= (x+1)^2$
$= x^2+2x + 1$
Hence, the correct answer is $ x^2+2x +1$.
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