Câu `a` chỗ `3'7` là `3/7` nhỉ?

`a)5/11 . 6/11:3/7`

`=30/121 . 7/3`

`=70/121`

`b)5/2+13/4:2-17/4`

`=5/2+13/8-17/4`

`=33/8-17/4`

`=-1/8`

`a, 5/11 . 6/11 : 3/7`

`= 5/11 . 6/11 . 7/3`

`=(5.6.7)/(11.11.3)`

`= 210/363`

`=70/121`

`b, 5/2 + 13/4 : 2 -17/4`

`=  5/2 + 13/4 . 1/2-17/4`

`=5/2 +13/8-17/4`

`=20/8+13/8-17/4`

`= 33/8 -17/4`

`=33/8 - 34/8`

`=-1/8`

`8/15-x:3/4=11/18`

`x:3/4=8/15-11/18`

`x:3/4=-7/90`

`x=-7/90 . 3/4`

`x=-7/120`

\(\dfrac{8}{15}-x:\dfrac{3}{4}=\dfrac{11}{18}\)

          \(x:\dfrac{3}{4}=\dfrac{8}{15}-\dfrac{11}{18}\)   

          \(x:\dfrac{3}{4}=-\dfrac{7}{90}\)

          \(x=-\dfrac{7}{90}.\dfrac{3}{4}\)

          \(x=-\dfrac{7}{120}\)

       Vậy \(x=-\dfrac{7}{120}\)

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

\(\Rightarrow\left(x-3\right)^{2^x}:\left(x-3\right)^x=1\)

\(\Rightarrow\left(x-3\right)^2:\left(x-3\right)^x=1\)

Mà kết quả ở đây bằng 1 nên chỉ có 1 phép chia duy nhất là \(1:1=1\)

Vậy \(\left(x-3\right)^2=\left(x-3\right)^x=1;\)

\(\Rightarrow\left(x-3\right)=\left(x-3\right)=1\) vì chỉ có lũy thừa của 1 mới bằng 1.

\(\Rightarrow x=3+1=4\)

cảm ơn ạ

\(A=\dfrac{10^{11}+1}{10^{12}-1}\)

\(\Rightarrow10A=\dfrac{10^{11}+1}{10^{12}-1}.10\)

\(\Rightarrow10A=\dfrac{10\left(10^{11}+1\right)}{10^{12}-1}\)

\(\Rightarrow10A=\dfrac{10^{12}-10}{10^{12}-1}\)

\(B=\dfrac{10^{10}+1}{10^{11}+1}\)

\(\Rightarrow10B=\dfrac{10^{10}+1}{10^{11}+1}.10\)

\(\Rightarrow10B=\dfrac{\left(10^{10}+1\right).10}{10^{11}+1}\)

\(\Rightarrow10B=\dfrac{10^{11}+10}{10^{11}+1}\)

Ta thấy:

 \(10^{12}-1>10^{12}-10>0\Rightarrow10A< 1\)

\(0< 10^{11}+1< 10^{11}+10\Rightarrow10B>1\)

Mà \(10A< 1;10B>1\)

\(\Rightarrow B>A\).

\(a.\dfrac{7}{8}+\dfrac{1}{2}\text{=}\dfrac{11}{8}\)

\(b.\dfrac{5}{6}+\left(-2\right)\text{=}\dfrac{-7}{6}\)

\(c.\dfrac{2}{5}+\dfrac{-3}{8}\text{=}\dfrac{1}{40}\)

\(d.\dfrac{5}{7}-\dfrac{3}{8}\text{=}\dfrac{19}{56}\)

\(e.\dfrac{3}{4}-\dfrac{1}{2}+\dfrac{7}{6}\text{=}\dfrac{17}{12}\)

`a. 7/8 + 1/2 = 7/8 + 4/8=(7+4)/8=11/8`

`b. 5/6 + (-2) =5/6 + (-12/6)=-7/6`

`c. 2/5 + -3/8   = 16/40 + (-15/40)=1/40`

`d. 5/7  - 3/8  = 40/56 - 21/56=19/56`

`e. 3/4 - 1/2 +7/6= 3/4 - 2/4 + 7/6= 1/4 + 7/6= 6/24 + 28/24= 34/24=17/12`

`(11/6 -5/8) xx 3/5 + 2/5 : 14/15`

`= (88/48-30/48) xx 3/5 + 2/5 xx 15/14`

`= 58/48xx 3/5 + 2/5 xx 15/14`

`=29/24 xx 3/5 + 2/5 xx 15/14`

`= 29/40+3/7`

`=323/280`

\(\left(\dfrac{29}{24}\right).\dfrac{3}{5}+\dfrac{3}{7}\) = \(\dfrac{29}{40}+\dfrac{3}{7}=\dfrac{323}{280}\)

\(\dfrac{a+b}{4}=a,b=\dfrac{10a+b}{10}\)

\(\dfrac{5a+5b}{20}=\dfrac{20a+2b}{20}\)

5a+5b=20a+2b

15a=3b

b=5a

Vậy a = 1 và b= 5

Lời giải:

Ta có:
$\overline{a,b}=\frac{a+b}{4}$

$\Rightarrow 4\overline{a,b}=a+b$

$\Rightarrow 4(a+\frac{b}{10})=a+b$

$\Rightarrow 4(10a+b)=10(a+b)$

$\Rightarrow 30a=6b$
$\Rightarrow b=5a$

Vì $b$ là số tự nhiên có 1 chữ số nên $5a=b<10$

$\Rightarrow a<2$

Vì $a$ là số tự nhiên nên $a=0$ hoặc $a=1$

Nếu $a=0$ thì $b=5a=0$. Số thập phân $0,0=0$ 

Nếu $a=1$ thì $b=5a=5$. Số thập phân $1,5$

Ta có \(3^{2^{4n}+1}\) + 2 = 3^{16n + 1} + 2 = 3¹⁶ⁿ . 3 + 2 = ( 3⁴ )⁴ⁿ . 3 + 2

= 81⁴ⁿ . 3 + 2 = ( 81⁴ )ⁿ . 3 + 2 = ( ...1 )ⁿ . 3 + 2 = ( ...1 ) . 3 + 2

= ( ...3 ) + 2 = ( ...5 )

Vì số có chữ số tận cùng là 5 chia hết cho 5 nên ( \(3^{2^{4n}+1}\) + 2 ) ⋮ 5

\(\dfrac{9}{23}+\dfrac{53}{3}+\dfrac{2}{69}+\left(-15\right)\)

\(=\dfrac{9.3}{23.3}+\dfrac{53.23}{3.23}+\dfrac{2}{69}+\dfrac{-15.69}{1.69}\)

\(=\dfrac{27}{69}+\dfrac{1219}{69}+\dfrac{2}{69}+\dfrac{-345}{69}\)

\(=\dfrac{903}{69}\)

\(=\dfrac{301}{23}\).

\(-\dfrac{3}{4}+\dfrac{5}{7}+\dfrac{7}{2}\)

\(=-\dfrac{21}{28}+\dfrac{20}{28}+\dfrac{98}{28}\)

\(=\dfrac{97}{28}\)