Rút gọn biểu thức `A=` `{x^3 – x^2 + 2}/{x^4 + 4}` (Bằng `2` cách)

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1. $\text{→ Cách 1 :}$

   $\text{- Ta có :}$

   $\text{A = $\dfrac{x³ – x² + 2}{x^4 + 4}$}$

   $\text{⇔ A = $\dfrac{x³ + x² – 2x² + 2}{x^4 + 4x^2 + 4 – 4x^2}$}$

   $\text{⇔ A = $\dfrac{ x²( x + 1 ) – 2( x + 1 )( x – 1 ) }{ ( x² + 2 ) – ( 2x )² }$}$

   $\text{⇔ A = $\dfrac{( x + 1 )( x² – 2x + 2 ) }{( x² + 2x + 2 )( x² – 2x + 2 ) }$}$

   $\text{⇔ A = $\dfrac{x + 1}{x² + 2x + 2}$}$

   $\text{→ Cách 2 : }$

   $\text{- Ta có :}$

   $\text{A = $\dfrac{x³ – x² + 2}{x^4 + 4}$}$

   $\text{⇔ A = $\dfrac{x³ + 1 – x² + 1}{ ( x² + 2x + 2 )( x² – 2x + 2 ) }$}$

   $\text{⇔ A = $\dfrac{ ( x + 1 )( x² – x + 1 ) – ( x + 1 )( x – 1 ) }{ ( x² + 2x + 2 )( x² – 2x + 2 ) }$}$

   $\text{⇔ A = $\dfrac{ ( x + 1 )( x² – x + 1 – x + 1 ) }{ ( x² + 2x + 2 )( x² – 2x + 2 ) }$}$

   $\text{⇔ A = $\dfrac{ ( x + 1 )( x² – 2x + 2 ) }{ ( x² + 2x + 2 )( x² – 2x + 2 ) }$}$

   $\text{⇔ A = $\dfrac{x + 1 }{x² + 2x + 2 }$ }$

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