Question

cho B=x+1/x-2+2/x+3-9x-3/x^2+x-6

a,tìm điều kiện xác định

b,chứng tỏ B=1-4/x+3

Answer 1

\(B=\dfrac{x+1}{x-2}+\dfrac{2}{x+3}-\dfrac{9x-3}{x^2+x-6}\)

\(=\dfrac{x+1}{x-2}+\dfrac{2}{x+3}+\dfrac{-9x+3}{\left(x-2\right)\left(x+3\right)}\) (1)

`a,`

`ĐKXĐ:`\(\left\{{}\begin{matrix}x-2\ne0\\x+3\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne2\\x\ne-3\end{matrix}\right.\)

`b,` 

(Tiếp tục từ (1))

\(=\dfrac{\left(x+1\right)\left(x+3\right)+2\left(x-2\right)-9x+3}{\left(x-2\right)\left(x+3\right)}\)

\(=\dfrac{x^2+4x+3+2x-4-9x+3}{\left(x-2\right)\left(x+3\right)}\)

`=(x^2 -3x+2)/((x-2)(x+3))`

`=((x-2)(x-1))/((x-2)(x+3))`

`=(x-1)/(x+3)`.