Question

Rút gọn:

 a) \(\frac{x^2-2x-8}{x^2+x-12}\)

b) \(\frac{x^4-5x^2+4}{x^4-x^2+4x-4}\)

Answer 1

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Answer 2

b)     \(\frac{x^4-5x^2+4}{x^4-x^2+4x-4}\)

\(=\frac{x^4-x^2-4x^2+4}{x^2\left(x^2-1\right)+4\left(x-1\right)}\)

\(=\frac{\left(x^2-1\right)\left(x^2-4\right)}{\left(x-1\right)\left(x^3+x^2+4\right)}\)

\(=\frac{\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)}{\left(x-1\right)\left(x^3+x^2+4\right)}\)

\(=\frac{\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)}{\left(x-1\right)\left(x+2\right)\left(x^2-x+2\right)}\)

\(=\frac{x^2-x-2}{x^2-x+2}\)