Question

Rút gọn bt :

\(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}\)

Answer 1

\(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}=\dfrac{x^4-x^2-4x^2+4}{x^4-x^2-9x^2+9}\)

\(=\dfrac{x^2.\left(x^2-1\right)-4.\left(x^2-1\right)}{x^2.\left(x^2-1\right)-9.\left(x^2-1\right)}=\dfrac{\left(x^2-1\right)\left(x^2-4\right)}{\left(x^2-1\right)\left(x^2-9\right)}\)

\(=\dfrac{x^2-4}{x^2-9}\)

Chúc bạn học tốt!!!

Answer 2

\(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}\)

\(=\dfrac{x^4-x^2-4x^2+4}{x^4-x^2-9x^2+9}\)

\(=\dfrac{x^2\left(x^2-1\right)-4\left(x^2-1\right)}{x^2\left(x^2-1\right)-9\left(x^2-1\right)}\)

\(=\dfrac{\left(x^2-1\right)\left(x^2-4\right)}{\left(x^2-1\right)\left(x^2-9\right)}\)

\(=\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}\)

Answer 3

Ta có: \(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}\)\(=\dfrac{x^4-x^2-4x^2+4}{x^4-x^2-9x^2+9}=\dfrac{x^2\left(x^2-1\right)-4\left(x^2-1\right)}{x^2\left(x^2-1\right)-9\left(x^2-1\right)}\)

\(=\dfrac{\left(x^2-1\right)\left(x^2-4\right)}{\left(x^2-1\right)\left(x^2-9\right)}\)\(=\dfrac{\left(x-2\right)\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}\).

Answer 4

\(\dfrac{x^4-5x^2+4}{x^4-10x^2+9}=\dfrac{x^4-\left(x^2+4x^2\right)+4}{x^4-\left(x^2+9x^2\right)+9}\\ \)

\(=\dfrac{x^4-x^2-4x^2+4}{x^4-x^2-9x^2+9}\\ \)

\(=\dfrac{x^4-x^2-\left(4x^2-4\right)}{x^4-x^2-\left(9x^2-9\right)}\)

\(=\dfrac{x^2-\left(x^2-1\right)-4\left(x^2-1\right)}{x^2-\left(x^2-1\right)-9\left(x^2-1\right)}\\ \)

\(=\dfrac{\left(x^2-4\right)\left(x^2-1\right)}{\left(x^2-9\right)\left(x^2-1\right)}\\ \)

\(=\dfrac{x^2-4}{x^2-9}\)