Question

[Hoàng Quyết Nguyễn]

rút gọn giúp mình phân thức này với ạ!

Answer 1

[ILoveMath]

\(A=\left(\dfrac{2-x}{2+x}-\dfrac{16}{4-x^2}-\dfrac{2+x}{2-x}\right)\)

\(\Rightarrow A=\left(\dfrac{\left(2-x\right)^2}{\left(2+x\right)\left(2-x\right)}-\dfrac{16}{\left(2+x\right)\left(2-x\right)}-\dfrac{\left(2+x\right)^2}{\left(2+x\right)\left(2-x\right)}\right)\)\(\Rightarrow A=\left(\dfrac{4-4x+x^2}{\left(2+x\right)\left(2-x\right)}-\dfrac{16}{\left(2+x\right)\left(2-x\right)}-\dfrac{4+4x+x^2}{\left(2+x\right)\left(2-x\right)}\right)\)

\(\Rightarrow A=\dfrac{4-4x+x^2-16-4-4x-x^2}{\left(2+x\right)\left(2-x\right)}\)

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

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

\(\Rightarrow A=\dfrac{-8}{2-x}\)

\(\Rightarrow A=\dfrac{8}{x-2}\)