\(\Leftrightarrow\dfrac{\sqrt{3}\sqrt{7}-\sqrt{7}}{1-\sqrt{3}}\)
\(\Leftrightarrow\dfrac{\sqrt{7}\left(\sqrt{3}-1\right)}{1-\sqrt{3}}\)
\(\Leftrightarrow-\sqrt{7}\)
rút gọn biểu thức
e) \(\dfrac{\sqrt{a}-a}{\sqrt{a}-1}\)
f)\(\dfrac{\sqrt{7-4\sqrt{3}}}{\sqrt{3}-2}\)
2) giải phương trình
a)\(\sqrt{\dfrac{2x-3}{x-1}=2}\)
b)\(\dfrac{\sqrt{2x-3}}{\sqrt{x-1}}=2\)
ai giúp e mấy câu này với ạ !!!
rút gọn biểu thức
a, \(\dfrac{1}{\sqrt{7-\sqrt{24}+1}}-\dfrac{1}{\sqrt{7+\sqrt{24}+1}}\)
b,\(\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}+\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}\)
c,\(\dfrac{4+\sqrt{7}}{3\sqrt{2}+\sqrt{4}+\sqrt{7}}+\dfrac{4-\sqrt{7}}{3\sqrt{7}-\sqrt{4}-\sqrt{7}}\)
1) rút gọn biểu thức sau :
a) \(\dfrac{x+2\sqrt{x}-3}{\sqrt{x}-1}\) b) \(\dfrac{4y+3\sqrt{y}-7}{4\sqrt{y}+7}\) c ) \(\dfrac{x\sqrt{y}-y\sqrt{x}}{\sqrt{x}-\sqrt{y}}\)
d) \(\dfrac{x-3\sqrt{x}-4}{x-\sqrt{x}-12}\) e) \(\dfrac{1+\sqrt{x}+\sqrt{y}+\sqrt{xy}}{1+\sqrt{y}}\) ( với x>0 , y>0 )
f) \(\sqrt{8-2\sqrt{15}}+\sqrt{5}+\sqrt{3}\) g) \(\sqrt{9-2\sqrt{4}}-\sqrt{9+2\sqrt{14}}\)
Tính:
a) \(\dfrac{6}{\sqrt{2}-\sqrt{3}+3}\)
b) \(\dfrac{1}{\sqrt{10}+\sqrt{15}+\sqrt{14}+\sqrt{21}}\)
c)\(\dfrac{1}{2+\sqrt{5}+2\sqrt{2}+\sqrt{10}}\)
d)\(\dfrac{2\sqrt{30}}{\sqrt{5}+\sqrt{6}+\sqrt{7}}\)
so sánh \(\dfrac{\sqrt{21}-\sqrt{13}}{35-2\sqrt{273}}+\dfrac{\sqrt{10}-\sqrt{5}}{16-10\sqrt{2}}\)với 1
rút gọn biểu thức
a) \(\dfrac{2-\sqrt{2}}{\sqrt{2}}\)
b) \(\dfrac{\sqrt{2}+\sqrt{3}}{2+\sqrt{6}}\)
c) \(\dfrac{a+\sqrt{a}}{\sqrt{a}}\)
d)\(\dfrac{3+\sqrt{3}}{1+\sqrt{a}}\)
ai giúp e mấy câu này với ạ , làm câu nào cũng được ạ !!!
Rút gọn:
a.\(\sqrt{21-6\sqrt6}+\sqrt{9+2\sqrt{18}}-2\sqrt{6+3\sqrt{3}}\)
b.\(\sqrt{4+\sqrt{15}}-\sqrt{7-3\sqrt{5}}\)
c.\(\sqrt{\dfrac{13}{4}+\sqrt{3}}\)\(-\sqrt{\dfrac{7}{4}-\sqrt{3}}\)
Tính:
a) \(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)
b) \(\dfrac{2}{\sqrt{6}-2}+\dfrac{2}{\sqrt{6}+2}+\dfrac{5}{\sqrt{6}}\)
c) \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
d) \(\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
Thực hiện các phép tính sau:
a. \(\dfrac{5\sqrt{3}-3\sqrt{5}}{\sqrt{5}-\sqrt{3}}-\dfrac{6}{\sqrt{15}+3}\)
b. \(\left(\sqrt{10+2\sqrt{21}}-\sqrt{10-2\sqrt{21}}\right)-\dfrac{4}{\sqrt{3}+1}\)
c. \(\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{18}+\sqrt{27}\right)\)
