12.194+6.437.2+3.369.4

=12.194+(6.2).437+(3.4).369

=12.194+12. 437+12.369

=12.(194+437+369)

=12.1000

=12000

a: \(61\cdot45+61\cdot23-68\cdot51\)

\(=61\left(45+23\right)-68\cdot51\)

\(=68\cdot61-68\cdot51\)

\(=68\left(61-51\right)=68\cdot10=680\)

b: \(3\cdot5^2-\left(75-4\cdot2^3\right)\)

\(=75-75+4\cdot8\)

\(=4\cdot8=32\)

c: \(36:\left\{2^2\cdot5-\left[30-\left(5-1\right)^2\right]\right\}\)

\(=\dfrac{36}{20-30+4^2}\)

\(=\dfrac{36}{-10+16}=\dfrac{36}{6}=6\)

d: \(\left(12\cdot49-3\cdot2^2\cdot7^2\right):\left(2020\cdot2021\right)\)

\(=\dfrac{\left(12\cdot49-12\cdot49\right)}{2020\cdot2021}=0\)

a: ĐKXĐ: \(x\notin\left\{4;-4\right\}\)

\(\dfrac{7}{4x+16}=\dfrac{7}{4\left(x+4\right)}=\dfrac{7\left(x-4\right)}{4\left(x+4\right)\left(x-4\right)}\)

\(\dfrac{11}{x^2-16}=\dfrac{11\cdot4}{4\left(x^2-16\right)}=\dfrac{44}{4\left(x-4\right)\left(x+4\right)}\)

b: \(\dfrac{6}{x\left(x+3\right)^2};\dfrac{x-3}{2x\left(x+3\right)^2}\)

ĐKXĐ: \(x\notin\left\{0;-3\right\}\)

\(\dfrac{6}{x\left(x+3\right)^2}=\dfrac{6\cdot2}{2x\left(x+3\right)^2}=\dfrac{12}{2x\left(x+3\right)^2}\)

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

c: \(\dfrac{-6}{1-x};\dfrac{3x}{x^2+x+1};\dfrac{x^2-3x+5}{x^3-1}\)

ĐKXĐ: \(x\ne1\)

\(-\dfrac{6}{1-x}=\dfrac{6}{x-1}=\dfrac{6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{6x^2+6x+6}{\left(x-1\right)\left(x^2+x+1\right)}\)

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

\(\dfrac{x^2-3x+5}{x^3-1}=\dfrac{x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)

d: \(\dfrac{17}{5x};\dfrac{24}{x-2y};\dfrac{x-y}{8y^2-2x^2}\)

ĐKXĐ: \(x\ne0;x\ne\pm2y\)

\(\dfrac{17}{5x}=\dfrac{17\cdot2\left(x-2y\right)\left(x+2y\right)}{5x\cdot2\cdot\left(x-2y\right)\left(x+2y\right)}=\dfrac{34\left(x^2-4y^2\right)}{10x\left(x-2y\right)\left(x+2y\right)}\)

\(\dfrac{24}{x-2y}=\dfrac{24\cdot10x\left(x+2y\right)}{10x\left(x-2y\right)\left(x+2y\right)}=\dfrac{240x\left(x+2y\right)}{10x\left(x-2y\right)\left(x+2y\right)}\)

\(\dfrac{x-y}{8y^2-2x^2}=\dfrac{-\left(x-y\right)}{2x^2-8y^2}=\dfrac{-\left(x-y\right)}{2\left(x-2y\right)\left(x+2y\right)}\)
\(=\dfrac{-5x\left(x-y\right)}{10x\left(x-2y\right)\left(x+2y\right)}=\dfrac{-5x^2+5xy}{10x\left(x-2y\right)\left(x+2y\right)}\)

\(52+3.\left(x-1\right)=61\)

            \(3.\left(x-1\right)=61-52\)

            \(3.\left(x-1\right)=9\)

                      \(x-1=9\div3\)

                      \(x-1=3\)

                               \(x=3+1\)

                               \(x=4\)

Đặt A = \(\dfrac{3}{1.6}+\dfrac{3}{6.11}+...+\dfrac{3}{61.66}\)

=> \(\dfrac{5}{3}A=\dfrac{5}{1.6}+\dfrac{5}{6.11}+...+\dfrac{5}{61.66}\)

=> \(\dfrac{5}{3}A=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{61}-\dfrac{1}{66}\)

=> \(\dfrac{5}{3}A=1-\dfrac{1}{66}=\dfrac{65}{66}\)

=> A = \(\dfrac{13}{22}\)

@nam nguyen

Đặt :

\(Â=\dfrac{3}{1.6}+\dfrac{3}{6.11}+...............+\dfrac{3}{61.66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{5}{1.6}+\dfrac{5}{6.11}+..............+\dfrac{5}{61.66}\)

\(\Leftrightarrow A\dfrac{5}{3}=1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+.........+\dfrac{1}{61}-\dfrac{1}{66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=1-\dfrac{1}{66}\)

\(\Leftrightarrow A.\dfrac{5}{3}=\dfrac{65}{66}\)

\(\Leftrightarrow A=\dfrac{13}{22}\)

`(x-3/5)xx3/8-5/8=1/6`

`(x-3/5)xx3/8=1/6+5/8`

`(x-3/5)xx3/8=4/24+15/24=19/24`

`x-3/5=19/24:3/8=19/9`

`x=19/9+3/5=122/45`

_______________________________________________________

`1 1/6-5/6:(x+1/4)=1/2`

`7/6-5/6:(x+1/4)=1/2`

`5/6:(x+1/4)=7/6-1/2=2/3`

`x+1/4=5/6:2/3=5/4`

`x=5/4-1/4=4/4=1`

a: \(\left(x-\dfrac{3}{5}\right)\cdot\dfrac{3}{8}-\dfrac{5}{8}=\dfrac{1}{6}\)

\(\Leftrightarrow\left(x-\dfrac{3}{5}\right)\cdot\dfrac{3}{8}=\dfrac{1}{6}+\dfrac{5}{8}=\dfrac{4}{24}+\dfrac{15}{24}=\dfrac{19}{24}\)

\(\Leftrightarrow x-\dfrac{3}{5}=\dfrac{19}{24}:\dfrac{3}{8}=\dfrac{19}{24}\cdot\dfrac{8}{3}=\dfrac{19}{9}\)

hay x=122/45

b: \(\Leftrightarrow\dfrac{7}{6}-\dfrac{5}{6}:\left(x+\dfrac{1}{4}\right)=\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{5}{6}:\left(x+\dfrac{1}{4}\right)=\dfrac{7}{6}-\dfrac{3}{6}=\dfrac{2}{3}\)

=>x+1/4=5/6:2/3=5/6x3/2=15/12=5/4

=>x=1