Đáp án:
$\rm x+1+4\dfrac{x-1}\\x-1+\dfrac{4}{x-1}+2\\\text{Áp dụng BĐT cosi:}\\x-1+\dfrac{4}{x-1} \geq 4\\\to x-1+\dfrac{4}{x-1}+2 \geq 6\\hay\,\, x+1+4\dfrac{x-1} \geq 6\\\text{Dấu "=" xảy ra khi:}\\x-1=\dfrac{4}{x-1}\\\leftrightarrow (x-1)^2=4\\\leftrightarrow x-1=2(do\,\,x>1)\\\leftrightarrow x=3$