Question

Rút gọn phân thức 6x-x^2-

5/5x^6-x^7

Answer 1

\(\dfrac{6x-x^2-5}{5x^6-x^7}\\ =\dfrac{-x^2+5x+x-5}{x^6\left(5-x\right)}\\ =\dfrac{\left(-x^2+5x\right)+\left(x-5\right)}{x^6\left(5-x\right)}\\ =\dfrac{-x\left(x-5\right)+\left(x-5\right)}{-x^6\left(x-5\right)}\\ =\dfrac{\left(-x+1\right)\left(x-5\right)}{-x^6\left(x-5\right)}\\ =\dfrac{-x+1}{-x^6}\)

Answer 2

\(\dfrac{-x^2+6x-5}{5x^6-x^7}\)

\(=\dfrac{x^2-6x+5}{x^7-5x^6}\)

\(=\dfrac{\left(x-1\right)\left(x-5\right)}{x^6\left(x-5\right)}\)

\(=\dfrac{x-1}{x^6}\)