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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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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