Question

Rút gọn phân thức :

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

\(2)\dfrac{a^{2x}-b^{2x}}{a^x-b^x}\)

Answer 1

1) Ta có: \(\dfrac{x\left|x-2\right|}{x^2-5x+6}\)

\(=\left[{}\begin{matrix}\dfrac{-x\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\left(x< 2\right)\\\dfrac{x\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\left(x>2\right)\end{matrix}\right.\)

\(=\left[{}\begin{matrix}\dfrac{-x}{x-3}\\\dfrac{x}{x-3}\end{matrix}\right.\)

2) Ta có: \(\dfrac{a^{2x}-b^{2x}}{a^x-b^x}\)

\(=\dfrac{\left(a^x\right)^2-\left(b^x\right)^2}{a^x-b^x}\)

\(=\dfrac{\left(a^x-b^x\right)\left(a^x+b^x\right)}{a^x-b^x}=a^x+b^x\)