\(A=\frac{\sqrt{x}+4}{\sqrt{x}+2};B=\left(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}\right):\frac{x+16}{\sqrt{x}+2}\)

a. rut gon B

b. Tim x nguyen de P = B(A-1) nguyen

giup minh voi a

Cho A = \(\left(\frac{x-\sqrt{x}+7}{x-4}+\frac{1}{\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}-2}-\frac{\sqrt{x}-2}{\sqrt{x}+2}-\frac{2\sqrt{x}}{x-4}\right)\)

a) Rut gon A

b) So sanh A voi \(\frac{1}{A}\)

1) Cho bieu thuc: \(B=\left(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}\right):\frac{x+16}{\sqrt{x}+2}\left(x\ge0,x\ne16\right)\)

a) Cho bieu thuc A= \(\frac{\sqrt{x}+4}{\sqrt{x}+2}\) ; voi cac cua bieu thuc A va B da cho, hay tim cac gia tri cua x nguyen de gia tri cua bieu thuc B(A;-1) la so nguyen

\(\left(\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{6}}{\sqrt{5}+\sqrt{b}}-\frac{2\sqrt{ab}}{a-b}\right)\left(\sqrt{a}+\sqrt{b}\right)=\)

voi A>B>0

Cho các số thực dương a,b,c,d. Chung minh rang \(\frac{b}{\left(a+\sqrt{b}\right)^2}+\frac{a}{\left(b+\sqrt{a}\right)^2}\ge\frac{\sqrt{bd}}{ac+\sqrt{bd}}\)

Giup mk voi cac ban

Cho B = \(\frac{1-ax}{1+ax}\sqrt{\frac{1+bx}{1-bx}}\) voi a<b<0

va x = \(\frac{1}{a}\sqrt{\frac{2a-b}{b}}\)

RUT GON B

cm voi moi so duong a b c thi

\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\ge\left(1+\sqrt{2}+\sqrt{3}\right)\left(\frac{1}{a+\sqrt{2b}+\sqrt{3a}}+\frac{1}{b+\sqrt{2c}+\sqrt{3a}}+\frac{1}{c+\sqrt{2a}+\sqrt{3b}}\right)\)

cho bieu thuc:P=\(\frac{\sqrt{x}}{\sqrt{x}-3}\)+\(\frac{2\sqrt{x}}{\sqrt{x}-3}\)--\(\frac{3x+9}{x-9}\) voi x>= 0;x#9 .a; Rut gon bieu thuc P . b; Tinh gia tri cua bieu thuc voi \(x=4-2\sqrt{3}\)

Rut gon bieu thuc sau

\(\sqrt{\frac{a}{b}}+\sqrt{ab}+\frac{a}{b}\sqrt{\frac{b}{a}}\) voi a > 0 va b > 0