\(\frac{x^4-5x^2+4}{x^4-10x^2+9}\) \(ĐKXĐ:x\ne\pm3\)
\(=\frac{x^4-4x^2-x^2+4}{x^4-9x^2-x^2+9}\)
\(=\frac{\left(x^4-4x^2\right)-\left(x^2-4\right)}{\left(x^4-9x^2\right)-\left(x^2-9\right)}\)
\(=\frac{x^2.\left(x^2-4\right)-\left(x^2-4\right)}{x^2.\left(x^2-9\right)-\left(x^2-9\right)}\)
\(=\frac{\left(x^2-1\right)\left(x^2-4\right)}{\left(x^2-1\right)\left(x^2-9\right)}\)
\(=\frac{x^2-4}{x^2-9}\)
\(\frac{x^4-5x^2+4}{x^4-10x^2+9}=\frac{x^4-x^2-4x^2+4}{x^4-x^2-9x^2+9}=\frac{x^2.\left(x^2-1\right)-4.\left(x^2-1\right)}{x^2.\left(x^2-1\right)-9.\left(x^2-1\right)}\)
\(=\frac{\left(x^2-4\right)\left(x^2-1\right)}{\left(x^2-1\right)\left(x^2-9\right)}=\frac{x^2-4}{x^2-9}\)
