Question

Bài 1: Cho Q= \(\frac{2}{x-1}+\frac{1}{\sqrt{x}-1}+\frac{1}{\sqrt{x}+1}\) ( x ≥0, x≠1)

a) Rút gọn Q

b) Tính Q khi x = 9

Bài 2: M= \(\frac{a+\sqrt{ab}}{b+\sqrt{ab}}+\frac{\sqrt{b}}{\sqrt{a}}\) ( a>0, b>0)

a)Rút gọn M

b) Tính M khi a = 3, b=12

(mink đag cần gấp)

Answer 1

Bài 1:

a) \(Q=\frac{2}{(\sqrt{x}-1)(\sqrt{x}+1)}+\frac{\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}+\frac{\sqrt{x}-1}{(\sqrt{x}+1)(\sqrt{x}-1)}\)

\(=\frac{2+2\sqrt{x}}{(\sqrt{x}+1)(\sqrt{x}-1)}=\frac{2(1+\sqrt{x})}{(\sqrt{x}-1)(\sqrt{x}+1)}=\frac{2}{\sqrt{x}-1}\)

b) Khi $x=9$ thì: \(Q=\frac{2}{\sqrt{9}-1}=\frac{2}{3-1}=1\)

Answer 2

Bài 2:

a)

\(M=\frac{\sqrt{a}(\sqrt{a}+\sqrt{b})}{\sqrt{b}(\sqrt{b}+\sqrt{a})}+\frac{\sqrt{b}}{\sqrt{a}}=\frac{\sqrt{a}}{\sqrt{b}}+\frac{\sqrt{b}}{\sqrt{a}}=\frac{a+b}{\sqrt{ab}}\)

b) Khi $a=3; b=12$ thì: \(M=\frac{3+12}{\sqrt{3.12}}=\frac{15}{\sqrt{36}}=\frac{15}{6}=\frac{5}{2}\)