a: \(A=4\cdot\dfrac{5}{2}\sqrt{x}-\dfrac{8}{3}\cdot\dfrac{3}{2}\sqrt{x}-\dfrac{4}{3x}\cdot\dfrac{3x}{8}\cdot\sqrt{x}\)

\(=10\sqrt{x}-4\sqrt{x}-\dfrac{1}{2}\sqrt{x}\)

\(=\dfrac{11}{2}\sqrt{x}\)

b: \(B=\dfrac{y}{2}+\dfrac{3}{4}\cdot\left|2y-1\right|-\dfrac{3}{2}\)

\(=\dfrac{y}{2}+\dfrac{3}{4}\left(1-2y\right)-\dfrac{3}{2}\)

=1/2y+3/4-3/2y-3/2

=-y-3/4

Lời giải:
$A=4.\sqrt{\frac{25}{4}}.\sqrt{x}-\frac{8}{3}.\sqrt{\frac{9}{4}}.\sqrt{x}-\frac{4}{3x}.\sqrt{\frac{9}{64}}.\sqrt{x^3}$

$=10\frac{x}-4\sqrt{x}-\frac{1}{2x}.x\sqrt{x}=10x-4x-\frac{1}{2}\sqrt{x}$

$=\frac{11}{2}\sqrt{x}$

\(A=4\sqrt{\dfrac{25x}{4}}-\dfrac{8}{3}\sqrt{\dfrac{9x}{4}}-\dfrac{4}{3x}\sqrt{\dfrac{9x^3}{64}}\)

\(A=4\left|\dfrac{5\sqrt{x}}{2}\right|-\dfrac{8}{3}\left|\dfrac{3\sqrt{x}}{2}\right|-\dfrac{4}{3x}\left|\dfrac{3x\sqrt{x}}{8}\right|\)

Vì \(x>0\) nên:

\(A=10\sqrt{x}-4\sqrt{x}-\dfrac{1}{2}\sqrt{x}=\dfrac{11\sqrt{x}}{2}\)

chào bạn kb nhé

minh giai nhu the nay xem dung ko nha:

x se la mu  2 :

nhu vay ta se duoc : 

\(\left(-8\right)^2\) = 64 { vi (- 8) . (- 8) = 64 vi am nham voi am se ra duong }

tuong tu : \(13^2\)= 169  ( vi 13 .13 = 169 )

 nen ta co  \(\frac{64}{169}=\frac{64}{169}\)

nen ta => so nguyen x con co the noi la mu x = 2

vay \(\frac{64}{169}=\left(-\frac{8}{13}\right)^2\)

a: \(\left(x+1\right)^2+\left(x+3\right)\left(x-2\right)-4x\)

\(=x^2+2x+1+x^2+x-6-4x\)

\(=2x^2-x-6\)

\(2+4+6+8+...+150=\frac{\left(150+2\right)\left[\left(150-2\right)\div2+1\right]}{2}\)

\(=\frac{152.75}{2}=76.75=5700\)

\(7+10+13+...+76=\frac{\left(76+7\right)\left[\left(76-7\right)\div3+1\right]}{2}\)

\(=\frac{83.24}{2}=83.12=996\)

\(49+64+81+...+169=7^2+8^2+9^2+...+13^2=584\)

a) Ta có: \(\sqrt{4-5x}=12\)

\(\Leftrightarrow4-5x=144\)

\(\Leftrightarrow5x=-140\)

hay x=-28

b) Ta có: \(\sqrt{10+\sqrt{3x}}=2+\sqrt{6}\)

\(\Leftrightarrow\sqrt{3x}+10=10+4\sqrt{6}\)

\(\Leftrightarrow\sqrt{3x}=4\sqrt{6}\)

\(\Leftrightarrow3x=96\)

hay x=32

c) Ta có: \(\sqrt{4x+20}-3\sqrt{x+5}+\dfrac{4}{3}\sqrt{9x+45}=6\)

\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+\dfrac{4}{3}\cdot3\sqrt{x+5}=6\)

\(\Leftrightarrow x+5=4\)

hay x=-1

b: \(\dfrac{\left(3x+2\right)^2-\left(x+2\right)^2}{x^3-x^2}\)

\(=\dfrac{\left(3x+2+x+2\right)\left(3x+2-x-2\right)}{x^2\left(x-1\right)}\)

\(=\dfrac{\left(4x+4\right)\cdot2x}{x^2\left(x-1\right)}\)

\(=\dfrac{8x\left(x+1\right)}{x^2\left(x-1\right)}=\dfrac{8}{x}\)