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

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1. $\text{→ Cách 1 :}$

   $\text{- Ta có :}$

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

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

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

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

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

   $\text{→ Cách 2 : }$

   $\text{- Ta có :}$

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

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

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

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

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

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

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