\(=\left(\dfrac{\sqrt{2}\left(\sqrt{6}-\sqrt{3}\right)}{2\left(\sqrt{2}-1\right)}+1\right).\dfrac{\sqrt{6}-2}{\left(\sqrt{6}+2\right)\left(\sqrt{6}-2\right)}\)
\(=\left(\dfrac{\left(\sqrt{6}-\sqrt{3}\right)}{\sqrt{2}\left(\sqrt{2}-1\right)}+1\right).\dfrac{\sqrt{6}-2}{6-4}\)
\(=\left(\dfrac{\left(\sqrt{6}-\sqrt{3}\right)}{2-\sqrt{2}}+1\right).\dfrac{\sqrt{6}-2}{2}\)
\(=\left(\dfrac{\left(\sqrt{6}-\sqrt{3}\right)\left(2+\sqrt{2}\right)}{\left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right)}+1\right).\dfrac{\sqrt{6}-2}{2}\)
\(=\left(\dfrac{\sqrt{6}}{4-2}+1\right).\dfrac{\sqrt{6}-2}{2}\)
\(=\left(\dfrac{\sqrt{6}}{2}+1\right).\dfrac{\sqrt{6}-2}{2}\)
\(=\dfrac{2+\sqrt{6}}{2}.\dfrac{\sqrt{6}-2}{2}=\dfrac{2\sqrt{6}-4+6-2\sqrt{6}}{4}=\dfrac{1}{2}\)

\(x+\dfrac{40}{27}=2\)
\(x=\dfrac{14}{27}\)

a)
\(=\sqrt{10\left(x+2\right)}=\sqrt{10}.\sqrt{x+2}\)
\(\sqrt{x+2}\ge0=>x+2\ge0=>x\ge-2\)
b)
\(=\dfrac{\sqrt{99}}{\sqrt{4x-1}}\)
\(=>4x-1>0=>4x>1=>x>\dfrac{1}{4}\)
c)
\(=\dfrac{\sqrt{-5x-10}}{\sqrt{2021}}=>-5x-10\ge0\)
\(=>-5\left(x+2\right)\ge0\)
\(=>x+2\ge0=>x\ge-2\)

a)
\(=\dfrac{22}{3}.\dfrac{23}{2}-\dfrac{22}{3}.\dfrac{20}{11}-\dfrac{3}{2}\)
\(=\dfrac{22}{3}\left(\dfrac{23}{2}-\dfrac{20}{11}\right)-\dfrac{3}{2}\)
\(=\dfrac{22}{3}.\dfrac{213}{22}-\dfrac{3}{2}=71-\dfrac{3}{2}=69,5\)
b)\(=\dfrac{10}{17}-\dfrac{5}{13}+\dfrac{7}{17}-\dfrac{8}{13}+\dfrac{11}{25}=1-1+\dfrac{11}{25}=\dfrac{11}{25}\)
b)
\(=0,25-\dfrac{9}{4}:\dfrac{1}{4}+\dfrac{3}{2}.1=0,25-9+\dfrac{3}{2}=-7,25\)
c)
\(=\dfrac{25}{9}+\dfrac{9}{4}-\dfrac{5}{6}=\dfrac{151}{36}\)

phân thức xác định khi
\(x^2+x-2\ne0\)
\(x^2+2x-x-2\ne0\)
\(x\left(x+2\right)-\left(x+2\right)\ne0\)
\(\left(x-1\right)\left(x+2\right)\ne0\)
\(x-1\ne0vàx+2\ne0\)
\(x\ne1\) và \(x\ne-2\)

a.      124 + (118 – x) = 217
                     118 - x  = 93
                            - x = - 25
                              x  = 25

b.      7x – 8 = 713
          7x      =721
            x      =103

c.       x- 36:18 = 12
          x- 2        =12
          x             =14

d.      (x- 36):18 = 12
           x-36        = 216
           x             = 252
          

e.      (x-47) -115 = 0
          x-47          = 115
          x               = 162

f.        315 + (146 – x) = 401
                      146-x     =86
                            -x     = -60
                             x     = 60

g.      (6x – 39 ) : 3 = 201
           6x - 39        = 603
           6x               = 642
             x               = 107

h.      23 + 3x = 5⁶ : 5³
         23 +3x   = 125
                3x    = 102
                  x=34

7045+2165:5-468
=7 045 + 433 - 468
=7010
(1268+427)x(5-769)
=1695x(-764)
= - 1 294 980

a)
=\(3.5.5+3.5.2-13=3.5\left(5+2\right)-13=15.7-13=105-13=92\)
b)
\(=5^3.2-25+2^3.5=5.25-5.5+8.5=5\left(25-5+8\right)=5.28=140\)
c)
\(6^2:9+50.2-3^3.3=36:9+100-3^4\)
=\(4+100-81\)=23

gọi số cần tìm là a
(a+1001)x3=99 999
a+1001=99 999 : 3
a+ 1001=33 333
a=33 333-1 001
a=32332

S=1+(2-3)+(-4+5)+(6-7)+(-8+9)+...+(-2020+2021)
S=1-1+1-1+1+...+1
S=1+0+0+...+0
S=1