Đáp án:
$a)-115$
Giải thích các bước giải:
$a)\left(\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}}\right)(\sqrt{6}+11)\\ =\left(\dfrac{15(\sqrt{6}-1)}{(\sqrt{6}+1)(\sqrt{6}-1)}+\dfrac{4(\sqrt{6}+2)}{(\sqrt{6}-2)(\sqrt{6}+2)}-\dfrac{12(3+\sqrt{6})}{(3-\sqrt{6})(3+\sqrt{6})}\right)(\sqrt{6}+11)\\ =\left(\dfrac{15(\sqrt{6}-1)}{5}+\dfrac{4(\sqrt{6}+2)}{2}-\dfrac{12(3+\sqrt{6})}{3}\right)(\sqrt{6}+11)\\ =\left(3(\sqrt{6}-1)+2(\sqrt{6}+2)-4(3+\sqrt{6})\right)(\sqrt{6}+11)\\ =\left(3\sqrt{6}-3+2\sqrt{6}+4-12+-4\sqrt{6})\right)(\sqrt{6}+11)\\ =(\sqrt{6}-11)(\sqrt{6}+11)\\ =6-121\\ =-115$
