SAO THỔ

a) \(\dfrac{2}{3}+\dfrac{4}{9}=\dfrac{6}{9}+\dfrac{4}{9}+\dfrac{6+3}{9}=\dfrac{10}{9}\)

b)\(\dfrac{1}{10}+\dfrac{2}{5}=\dfrac{1}{10}+\dfrac{4}{10}=\dfrac{1+4}{10}=\dfrac{5}{10}=\dfrac{1}{2}\)

c) \(\dfrac{7}{22}-\dfrac{3}{11}=\dfrac{7}{22}-\dfrac{6}{22}=\dfrac{7-6}{22}=\dfrac{1}{22}\)

d) \(\dfrac{5}{6}-\dfrac{5}{12}=\dfrac{10}{12}-\dfrac{5}{12}=\dfrac{10-5}{12}=\dfrac{5}{12}\)

a) \(\dfrac{3}{22}\times\dfrac{3}{11}\times22\)

\(=\dfrac{3}{22}\times\dfrac{3}{11}\times\dfrac{22}{1}\)

\(=\dfrac{3\times3\times22}{22\times11\times1}\)

\(=\dfrac{9}{11}\)

b) \(\left(\dfrac{1}{3}+\dfrac{1}{6}\right)\times\dfrac{2}{5}\)

\(=\left(\dfrac{2}{6}+\dfrac{1}{6}\right)\times\dfrac{2}{5}\)

\(=\dfrac{3}{6}\times\dfrac{2}{5}\)

\(=\dfrac{1}{2}\times\dfrac{2}{5}\)

\(=\dfrac{2}{10}\)

\(=\dfrac{1}{5}\)

a: =3/22*22*3/11

=3*3/11

=9/11

b: =(2/6+1/6)*2/5

=1/2*2/5

=1/5

\(\dfrac{-15}{22}\)

= - \(\dfrac{15}{22}\)

c: 2/5(1/2+3/2)^2=2/5*2^2=2/5*4=8/5

a: 6^100=2^100*3^100

b: 125^22=5^66

`@` `\text {Ans}`

`\downarrow`

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

`=> (x-3)5 = (2x+1)3`

`=> 5x-15 = 6x+3`

`=> 5x-6x = 15+3`

`=> -x=18`

`=> x=-18`

\(\dfrac{x+1}{22}=\dfrac{6}{x}\)

`=> (x+1)x = 22*6`

`=> (x+1)x = 132`

`=> x^2 + x = 132`

`=> x^2+x-132=0`

`=> (x-11)(x+12)=0`

`=>`\(\left[{}\begin{matrix}x-11=0\\x+12=0\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=11\\x=-12\end{matrix}\right.\)

\(\dfrac{2x-1}{2}=\dfrac{5}{x}\)

`=> (2x-1)x = 2*5`

`=> 2x^2 - x =10`

`=> 2x^2 - x - 10 =0`

`=> 2x^2 + 4x - 5x - 10 =0`

`=> (2x^2 + 4x) - (5x+10)=0`

`=> 2x(x+2) - 5(x+2)=0`

`=> (2x-5)(x+2)=0`

`=>`\(\left[{}\begin{matrix}2x-5=0\\x+2=0\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}2x=5\\x=-2\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-2\end{matrix}\right.\)

\(\dfrac{2x-1}{21}=\dfrac{3}{2x+1}\)

`=> (2x-1)(2x+1)=21*3`

`=> 4x^2 + 2x - 2x - 1 = 63`

`=> 4x^2 - 1=63`

`=> 4x^2 - 1 - 63=0`

`=> 4x^2 - 64 = 0`

`=> 4(x^2 - 16)=0`

`=> 4(x^2 + 4x - 4x - 16)=0`

`=> 4[(x^2+4x)-(4x+16)]=0`

`=> 4[x(x+4)-4(x+4)]=0`

`=> 4(x-4)(x+4)=0`

`=>`\(\left[{}\begin{matrix}x-4=0\\x+4=0\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

\(\dfrac{2x+1}{9}=\dfrac{5}{x+1}\)

`=> (2x+1)(x+1) = 9*5`

`=> (2x+1)(x+1)=45`

`=> 2x^2 + 2x + x + 1 = 45`

`=> 2x^2 + 3x + 1 =45`

`=> 2x^2 + 3x + 1 - 45 =0`

`=> 2x^2+3x-44=0`

`=> 2x^2 + 11x - 8x - 44=0`

`=> (2x^2 +11x) - (8x+44)=0`

`=> x(2x+11) - 4(2x+11)=0`

`=> (x-4)(2x+11)=0`

`=>`\(\left[{}\begin{matrix}x-4=0\\2x+11=0\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=4\\2x=-11\end{matrix}\right.\)

`=>`\(\left[{}\begin{matrix}x=4\\x=-\dfrac{11}{2}\end{matrix}\right.\)

\(\dfrac{x-3}{3}=\dfrac{2x+1}{5}\\ \left(x-3\right)\cdot5=\left(2x+1\right)\cdot3\\ x5-15=6x+3\\ x5-6x=3+15\\ -x=18\\ \Rightarrow x=-18\)

\(\dfrac{x+1}{22}=\dfrac{6}{x}\\ \left(x+1\right)\cdot x=6\cdot22\\ \left(x+1\right)\cdot x=2\cdot3\cdot2\cdot11\\ \left(x+1\right)\cdot x=12\cdot11\\ \Rightarrow x=11\)

\(\dfrac{2x-1}{21}=\dfrac{3}{2x+1}\\ \left(2x-1\right)\cdot\left(2x+1\right)=21\cdot3\\ \left(2x-1\right)\cdot\left(2x+1\right)=7\cdot3\cdot3\\ \left(2x-1\right)\cdot\left(2x+1\right)=7\cdot9\\ \Rightarrow2x+1=9\\ 2x=8\\ x=4\)

mik cần gấp nên bn nào giúp mik với ạk

1, \(12:\left(\dfrac{3}{4}-\dfrac{5}{6}\right)^2=12:\left(-\dfrac{1}{12}\right)^2=12:\dfrac{1}{144}=1728\)

2, \(\dfrac{7}{23}.\left(-\dfrac{8}{6}-\dfrac{45}{18}\right)=\dfrac{7}{23}.-\dfrac{23}{6}=-\dfrac{7}{6}\)

\(a,\dfrac{2}{13}\times\dfrac{22}{5}\times\dfrac{13}{2}\\ =\left(\dfrac{2}{13}\times\dfrac{13}{2}\right)\times\dfrac{22}{5}\\ =1\times\dfrac{22}{5}=\dfrac{22}{5}\\ b,\dfrac{3}{5}\times\dfrac{6}{7}+\dfrac{6}{7}\times\dfrac{3}{5}\\ =\dfrac{3}{5}\times\left(\dfrac{6}{7}+\dfrac{6}{7}\right)\\ =\dfrac{3}{5}\times\dfrac{12}{7}=\dfrac{36}{35}\)

\(a,=\left(\dfrac{2}{13}\times\dfrac{13}{2}\right)\times\dfrac{22}{5}=\dfrac{22}{5}\\ b,=\dfrac{3}{5}\times\left(\dfrac{6}{7}+\dfrac{6}{7}\right)\\ =\dfrac{3}{5}\times\dfrac{12}{7}\\ =\dfrac{36}{35}\)

a: \(=\dfrac{11}{21}+\dfrac{10}{21}+\dfrac{-2}{7}+\dfrac{-5}{7}-\dfrac{6}{5}=\dfrac{-6}{5}\)

b: \(=\left[0.25\cdot\left(-4\right)\right]^5\cdot\left(-\dfrac{50}{9}\right)\)

=50/9

c: \(=\dfrac{3}{22}\left(19+\dfrac{1}{7}+2+\dfrac{6}{7}\right)-6\)

\(=\dfrac{3}{22}\cdot22-6=3-6=-3\)