Question

\(\dfrac{x-2}{x+2}-\dfrac{x}{x-2}+\dfrac{8}{x^2-4}\)

\(\dfrac{2x}{x^2+2x^{ }}-\dfrac{8}{x^2-4}+\dfrac{2}{x-2}\)

\(\dfrac{2}{x-2}+\dfrac{3}{x-3}+\dfrac{3x-20}{\left(x-2\right)\left(x-3\right)}\)

giải thích cặn kẽ giúp mình nha đừng rút gọn bước nào

dài cũng được giúp mình đi

Answer 1

\(\dfrac{x-2}{x+2}-\dfrac{x}{x-2}+\dfrac{8}{x^2-4}=\dfrac{x-2}{x+2}+\dfrac{-x}{x-2}+\dfrac{8}{\left(x+2\right)\left(x-2\right)}=\dfrac{\left(x-2\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}+\dfrac{-x\cdot\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}+\dfrac{8}{\left(x+2\right)\left(x-2\right)}=\dfrac{\left(x-2\right)\left(x-2\right)-x\cdot\left(x+2\right)+8}{\left(x+2\right)\left(x-2\right)}=\dfrac{x^2-4x+4-x^2-2x+8}{\left(x+2\right)\left(x-2\right)}=\dfrac{12-6x}{\left(x+2\right)\left(x-2\right)}=\dfrac{6\left(2-3x\right)}{x^2-4}\)mỏi tay 1 bài này thôi lúc khác làm tiếp