Question

Câu 10: Rút gọn biểu thức:\(\dfrac{1-\dfrac{7}{x}+\dfrac{10}{x^2}}{1-\dfrac{25}{x^2}}\).

Answer 1

\(\dfrac{1-\dfrac{7}{x}+\dfrac{10}{x^2}}{1-\dfrac{25}{x^2}}=\left(1-\dfrac{7}{x}+\dfrac{10}{x^2}\right):\left(1-\dfrac{25}{x^2}\right)\)

\(=\dfrac{x^3-7x^2+10x}{x^3}:\dfrac{x^2-25}{x^2}\)

\(=\dfrac{(x^3-7x^2+10x).x^2}{x^3.\left(x-5\right)\left(x+5\right)}\)

\(=\dfrac{x^5-7x^4+10x^3}{x^3.\left(x-5\right)\left(x+5\right)}\)

\(=\dfrac{x^3\left(x^2-7x+10\right)}{x^3\left(x-5\right)\left(x+5\right)}\)

\(=\dfrac{x^2-7x+10}{\left(x-5\right)\left(x+5\right)}\)