\(=\dfrac{\sqrt{x}+3+2\sqrt{x}}{x-9}\cdot\dfrac{2\left(\sqrt{x}+3\right)}{\sqrt{x}+1}\)
\(=\dfrac{3\left(\sqrt{x}+1\right)\cdot2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}=\dfrac{6}{\sqrt{x}-3}\)
Rút gọn
\(\dfrac{6}{\sqrt{5}+1}+\sqrt{\dfrac{2}{3-\sqrt{5}}}-\dfrac{10}{\sqrt{5}}\)
B1. Với \(x\ge0,x\ne4.Chobiểuthức\)
\(A=\dfrac{x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}-\dfrac{1}{2-\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(B=\dfrac{1}{x\sqrt{x}+27}\)
a, tính giá trị biểu thức khi B= 1/4
b, Rút gọn A
c, Tìm giá trị của x để A>1/2
d, Với C= B : A. Tìm GTLN C
Rút gọn \(P=\left(\dfrac{x-3\sqrt{x}}{x-9}-1\right):\left(\dfrac{9-x}{x+\sqrt{x}-6}-\dfrac{\sqrt{x}-3}{2-\sqrt{x}}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)rồi tìm x thuộc Z để P thuộc Z.
\(\left(\dfrac{x+2\sqrt{x}-7}{x-9}+\dfrac{\sqrt{x}+1}{3-\sqrt{x}}\right):\left(\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-1}\right)\)
\(\dfrac{\sqrt{a}+3}{\sqrt{a}-2}-\dfrac{\sqrt{a}-1}{\sqrt{a}+2}+\dfrac{4\sqrt{a}-4}{4-a}\)
RÚT GONJ
\(\left(\dfrac{x+2\sqrt{x}+7}{x-9}+\dfrac{\sqrt{x}-1}{3-\sqrt{x}}\right):\left(\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-1}\right)\) RÚT GỌN
Rút gọn : \(\dfrac{2\sqrt{x}-9}{\left(\sqrt{x-2}\right)\left(\sqrt{x-3}\right)}-\dfrac{\sqrt{x}+3}{\sqrt{x}-2}-\dfrac{2\sqrt{x}+1}{3-\sqrt{x}}\)
Rút gọn biểu thức sau:
\(\sqrt{12+6\sqrt{3}}-\sqrt{3}\)
\(\left(\dfrac{1}{2\sqrt{x}}-\dfrac{\sqrt{x}}{2}\right)^2\times\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right)\)
28. A=\(\left(\dfrac{x-3\sqrt{x}}{x-9}-1\right):\left(\dfrac{9-x}{x+\sqrt{x}-6}+\dfrac{\sqrt{x}-3}{\sqrt{x}-2}-\dfrac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)
a. rút gọn A
b. tính A với x = \(7-4\sqrt{3}\)
c. tìm x khi A=3
40. B=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{2\sqrt{x}}{\sqrt{x}-3}-\dfrac{3x+9}{x-9}\right).\left(\dfrac{\sqrt{x}-2}{3}+1\right)\)
b. Rút gọn B
RÚT GỌN P:
P=\(\left(2+\dfrac{\sqrt{X}-1}{2\sqrt{X}-3}\right):\left(\dfrac{6\sqrt{X}+1}{2X-\sqrt{X}-3}+\dfrac{\sqrt{X}}{\sqrt{X}+1}\right)\)
Rút gọn các biểu thức sau:
\(C=\left(\dfrac{\sqrt{x}+1}{x-4}-\dfrac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right).\dfrac{x\sqrt{x}+2x-4\sqrt{x}-8}{\sqrt{x}-2}\)
(với \(x\ge0,x\ne4,x\ne9\))
\(D=\left(\dfrac{\sqrt{x}+2}{x-9}-\dfrac{\sqrt{x}-2}{x+6\sqrt{x}+9}\right).\dfrac{x\sqrt{x}+3x-9\sqrt{x}-27}{\sqrt{x}-2}\)
(với \(x\ge0,x\ne4,x\ne9\))
