a, ĐKXĐ: \(x\notin\left\{-2;\pm3\right\}\)
\(B=\left(\frac{21}{\left(x-3\right)\left(x+3\right)}+\frac{x-4}{x-3}-\frac{x-1}{x+3}\right):\frac{x+3-1}{x+3}\\ =\frac{21+\left(x-4\right)\left(x+3\right)-\left(x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\cdot\frac{x+3}{x+2}\\ =\frac{21+x^2-x-12-\left(x^2-4x+3\right)}{x-3}\cdot\frac{1}{x+2}\\ =\frac{x^2-x+9-x^2+4x-3}{\left(x-3\right)\left(x+2\right)}\\ =\frac{3x+6}{\left(x-3\right)\left(x+2\right)}\\ =\frac{3\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}=\frac{3}{x-3}\)
b, Ta có:
\(\left|2x+1\right|=5\Leftrightarrow\left\{{}\begin{matrix}2x+1=5\\2x+1=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\x=-3\left(ktm\right)\end{matrix}\right.\)
Suy ra, với \(x=2\), ta được:
\(B=\frac{3}{2-3}=\frac{3}{-1}=-3\)
c, Để \(B=\frac{-3}{5}\) thì:
\(\frac{3}{x-3}=\frac{-3}{5}\\ \Leftrightarrow\frac{-3}{3-x}=\frac{-3}{5}\\ \Leftrightarrow3-x=5\Leftrightarrow x=-2\left(ktm\right)\)
Hay không có giá trị nào sao cho \(B=\frac{-3}{5}\).
d, Do 3>0 nên để B<0 thì: \(x-3< 0\Leftrightarrow x< 3\).
Kết hợp với ĐKXĐ, ta có điều kiện: \(\left\{{}\begin{matrix}x< 3\\x\notin\left\{-2;-3\right\}\end{matrix}\right.\)
Chúc bạn học tốt nha.
