Làm
\(A=\left(\frac{8}{x+1}-\frac{12}{2x+1}\right):\left(2-\frac{x+3}{x+1}\right)\left(x\ne-1,x\ne\frac{-1}{2},x\ne\right)\)
\(A=\frac{16x+8-12x-12}{\left(x+1\right)\left(2x+1\right)}:\frac{2x+2-x-3}{x+1}\)
\(A=\frac{4x-4}{\left(x+1\right)\left(2x+1\right)}:\frac{x-1}{x+1}=\frac{4\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(2x+1\right)\left(x-1\right)}=\frac{4}{2x+1}\)
Kl:........
b) \(A=\frac{4}{2x+1}=\frac{4}{2.\frac{1}{2}+1}=\frac{4}{1+1}=\frac{4}{2}=2\)
KL:..........
c)Để A nguyên thì \(\frac{4}{2x+1}nguy\text{ê}n\)
mà \(xnguy\text{ê}nn\text{ê}n2x+1nguy\text{ê}n\)
=> 2x+1\(\in\text{Ư}\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)
mà 2x+1 lẻ nên 2x+1\(\in\left\{-1;1\right\}\)
=> \(x\in\left\{-1;0\right\}\)
KL:...............
