Question

Quy đồng mẫu thức các phân thức:

a,\(\dfrac{1}{x+2}\),\(\dfrac{8}{2x-x^2}\)

Answer 1

Ta có:

\(\dfrac{8}{2x-x^2}=\dfrac{8}{x\left(2-x\right)}=\dfrac{-8}{x\left(x-2\right)}\)

MTC: \(x\left(x-2\right)\left(x+2\right)\)

\(\Rightarrow\dfrac{1}{x+2}=\dfrac{x\left(x-2\right)}{x\left(x-2\right)\left(x+2\right)}=\dfrac{x^2-2x}{x\left(x-2\right)\left(x+2\right)}\)

\(\Rightarrow\dfrac{8}{2x-x^2}=\dfrac{8}{x\left(2-x\right)}=\dfrac{-8}{x\left(x-2\right)}=\dfrac{-8\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)}=\dfrac{-8x-16}{x\left(x-2\right)\left(x+2\right)}\)