3 ?

\(\dfrac{13}{4}>x>\dfrac{5}{2}\)

\(\Leftrightarrow\dfrac{13}{4}>x>\dfrac{10}{4}\)

\(\Leftrightarrow x\in\left\{\dfrac{11}{4};\dfrac{12}{4}\right\}\)

D.2

(A)

Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

Ta có: \(\dfrac{4a+3c}{4b+3d}=\dfrac{4bk+3dk}{4b+3d}=k\)

\(\dfrac{4a-3c}{4b-3d}=\dfrac{4bk-3dk}{4b-3d}=k\)

Do đó: \(\dfrac{4a+3c}{4b+3d}=\dfrac{4a-3c}{4b-3d}\)

Bài 2: 

\(=\dfrac{28}{25}\cdot\dfrac{15}{7}\cdot5=\dfrac{75}{25}\cdot4=12\)

Bài 1: 

a: \(x+\dfrac{7}{8}=\dfrac{13}{2}:4=\dfrac{13}{8}\)

nên x=13/8-7/8=6/8=3/4

b: \(x:\dfrac{5}{3}=\dfrac{6}{5}-\dfrac{2}{3}=\dfrac{18-10}{15}=\dfrac{8}{15}\)

nên \(x=\dfrac{8}{15}\cdot\dfrac{5}{3}=\dfrac{8}{9}\)

a: \(A=\sqrt{x}+\dfrac{\sqrt{x}\left(1+2\sqrt{x}\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}=\sqrt{x}+\dfrac{2\sqrt{x}+1}{\sqrt{x}+1}\)

Khi x=4 thì \(A=2+\dfrac{2\cdot2+1}{2+1}=2+\dfrac{5}{3}=\dfrac{11}{3}\)

b: Khi x=(2-căn 3)^2 thì \(A=2-\sqrt{3}+\dfrac{2\left(2-\sqrt{3}\right)+1}{2-\sqrt{3}+1}\)

\(=2-\sqrt{3}+\dfrac{4-2\sqrt{3}+1}{3-\sqrt{3}}\)

\(=2-\sqrt{3}+\dfrac{5-2\sqrt{3}}{3-\sqrt{3}}\)

\(=\dfrac{\left(2-\sqrt{3}\right)\left(3-\sqrt{3}\right)+5-2\sqrt{3}}{3-\sqrt{3}}\)

\(=\dfrac{6-2\sqrt{3}-3\sqrt{3}+3+5-2\sqrt{3}}{3-\sqrt{3}}\)

\(=\dfrac{14-7\sqrt{3}}{3-\sqrt{3}}\)

d: A=2

=>\(\dfrac{x+\sqrt{x}+2\sqrt{x}+1}{\sqrt{x}+1}=2\)

=>\(x+3\sqrt{x}+1=2\left(\sqrt{x}+1\right)=2\sqrt{x}+2\)

=>\(x+\sqrt{x}-1=0\)

=>\(\left[{}\begin{matrix}\sqrt{x}=\dfrac{-1+\sqrt{5}}{2}\left(nhận\right)\\\sqrt{x}=\dfrac{-1-\sqrt{5}}{2}\left(loại\right)\end{matrix}\right.\Leftrightarrow x=\dfrac{6-2\sqrt{5}}{4}=\dfrac{3-\sqrt{5}}{2}\)

ĐKXĐ: x>0

a:Sửa đề: \(A=\frac{x}{\sqrt{x}+1}+\frac{\sqrt{x}+2x}{x+\sqrt{x}}\)

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

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

\(=\frac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}+1}=\sqrt{x}+1\)

Thay x=4 vào A, ta được:

\(A=\sqrt4+1=2+1=3\)

b: Thay \(x=\left(2-\sqrt3\right)^2\) vào A, ta được:

\(A=\sqrt{\left(2-\sqrt3\right)^2}+1\)

\(=2-\sqrt3+1=3-\sqrt3\)

c: Sửa đề: \(x=4-2\sqrt3\)

Thay \(x=4-2\sqrt3\) vào A, ta được:

\(A=\sqrt{4-2\sqrt3}+1\)

\(=\sqrt{\left(\sqrt3-1\right)^2}+1\)

\(=\sqrt3-1+1=\sqrt3\)

d: A=2

=>\(\sqrt{x}+1=2\)

=>\(\sqrt{x}=1\)

=>x=1(nhận)

e: A>1

=>\(\sqrt{x}+1>1\)

=>\(\sqrt{x}>0\)

=>x>0

A đâu em?

\(A=\dfrac{x}{\sqrt{x}+1}+\dfrac{\sqrt{x}+2x}{x+\sqrt{x}}\)