Tính: a) A= \(\frac{1+2a}{1+\sqrt{1+2a}}+\frac{1-2a}{1-\sqrt{1-2a}}\)với a= \(\frac{\sqrt{3}}{4}\)

b) B= \(\frac{x\sqrt{x}-2x+28}{x-3\sqrt{x}-4}-\frac{\sqrt{x}-4}{\sqrt{x}+1}+\frac{\sqrt{x}+8}{4-\sqrt{x}}\)với 0 < x khác 16)

B=1+\(\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right).\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)

a)Rút gon B

b)Tìm a để B=\(\frac{\sqrt{6}}{1+\sqrt{6}}\)

c)CMR B>\(\frac{2}{3}\)

Cho biểu thức \(A=1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right).\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)

a, Rút gọn A

b, Tìm a để \(A=\frac{\sqrt{6}}{1+\sqrt{6}}\)

c,Chứng minh \(A>\frac{2}{3}\)

\(A=1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right).\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)

a) Rút gọn A

b) Tìm a để \(A=\frac{\sqrt{6}}{1+\sqrt{6}}\)

c) Chứng minh rằng \(A>\frac{2}{3}\)

\(A=1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right)\cdot\frac{a-\sqrt{a}}{2\sqrt{a}-1} \)

a. Rút gọn A
b) Tìm a để \(A=\frac{\sqrt{6}}{1+\sqrt{6}}\)

C)  CHỨNG MINH RẰNG A > \(\frac{2}{3}\)

Cho A=\(1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right)\times\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)

a> Rút gọc A

b> tìm a để a=\(\frac{6}{1+\sqrt{6}}\)

Rút gọn:
A= \(1+\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right).\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)

P= 1+\(\left(\frac{2a+\sqrt{a}-1}{1-a}-\frac{2a\sqrt{a}-\sqrt{a}+a}{1-a\sqrt{a}}\right)\).\(\frac{a-\sqrt{a}}{2\sqrt{a}-1}\)

a. Rút gọn P

b.cho P=\(\frac{\sqrt{6}}{1+\sqrt{6}}\) tìm giá trị biểu thức

c C/M P>\(\frac{2}{3}\)

​\(\frac{a-9}{\sqrt{a}-1}\)​: (\(\frac{2a-2}{a\sqrt{a}-1}\)​-\(\frac{\sqrt{a}-1}{a+\sqrt{a}+1}\))