Câu 31:
\(A=\frac{x\left(x^2+12\right)-6x^2-8}{x-2}\)
\(=\frac{x^3-6x^2+12x-8}{x-2}\)
\(=\frac{\left(x-2\right)^3}{x-2}=\left(x-2\right)^2\)
=>Chọn D
Câu 32: \(B=\frac{\left(x+1\right)^2-\left(x-1\right)^2}{\left(x-y\right)^2-\left(x+y\right)^2}\)
\(=\frac{\left(x+1-x+1\right)\left(x+1+x-1\right)}{\left(x-y-x-y\right)\left(x-y+x+y\right)}=\frac{2\cdot2x}{-2y\cdot2x}=\frac{2}{-2y}=-\frac{1}{y}\)
=>Chọn B
Câu 33: \(\frac{1}{x+1}+\frac{1}{x+2}-\frac{1}{\left(x+1\right)\left(x+2\right)}\)
\(=\frac{x+2+x+1-1}{\left(x+1\right)\left(x+2\right)}=\frac{2x+2}{\left(x+1\right)\left(x+2\right)}=\frac{2}{x+2}\)
=>Chọn D
Câu 34: \(A=\frac{x}{x^2+x+1}-\frac{2x+1}{1-x^3}\)
\(=\frac{x\left(x-1\right)+2x+1}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{1}{x-1}\)
=>Chọn A
