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4 tháng 11 2021

\(\Rightarrow n=-4\)

4 tháng 11 2021

\(=>\) n = -4

17 tháng 8 2017

\(\left\{{}\begin{matrix}1-\dfrac{2}{3}=\dfrac{1}{3}\\1-\dfrac{3}{4}=\dfrac{1}{4}\\1-\dfrac{4}{5}=\dfrac{1}{5}\\1-\dfrac{9}{10}=\dfrac{1}{10}\end{matrix}\right.\)

Vì:

\(\dfrac{1}{3}>\dfrac{1}{4}>\dfrac{1}{5}>...>\dfrac{1}{10}\)

nên:

\(\dfrac{2}{3}< \dfrac{3}{4}< \dfrac{4}{5}< ...< \dfrac{9}{10}\)

a)

Ta có:

\(\)\(\left\{{}\begin{matrix}\dfrac{3}{4}=\dfrac{2+1}{3+1}\\\dfrac{4}{5}=\dfrac{3+1}{4+1}\\\dfrac{5}{6}=\dfrac{4+1}{5+1}\\\dfrac{9}{10}=\dfrac{8+1}{9+1}\end{matrix}\right.\)

Suy ra quy luật:

Phân số tiếp theo chính là tử của p/s ban đầu +1/mẫu của p/s ban đầu +1

Vậy phân số sau phân số \(\dfrac{a}{b}\)\(\dfrac{a+1}{b+1}\)

So sánh :

\(\dfrac{a}{b}\)\(\dfrac{a+1}{b+1}\)

\(\dfrac{a}{b}=\dfrac{a\left(b+1\right)}{b\left(b+1\right)}=\dfrac{ab+a}{b^2+b}\)

\(\dfrac{a+1}{b+1}=\dfrac{b\left(a+1\right)}{b\left(b+1\right)}=\dfrac{ab+b}{b^2+b}\)

Vậy cần so sánh:

\(\dfrac{ab+a}{b^2+b}\) với \(\dfrac{ab+b}{b^2+b}\)

Cần so sánh:

\(ab+a\)\(ab+b\)

Cần so sánh \(a\) với \(b\)
Nếu \(a>b\Rightarrow\dfrac{a}{b}>\dfrac{a+1}{b+1}\)

Nếu \(a< b\Rightarrow\dfrac{a}{b}< \dfrac{a+1}{b+1}\)

Nếu \(a=b\) \(\Rightarrow\dfrac{a}{b}=\dfrac{a+1}{b+1}=1\)

Còn cách khác ngắn hơn nhưng lười làm lắm :v

17 tháng 8 2017

sao ko làm cách ngắn ngay từ đầu :(

12 tháng 11 2021

1.
a)10/7
b) 1
c) 3
d) 3/4
e) -1
2.
a)-3/8
b)x= 3 và x=-2
c)x=10 và x=-20

12 tháng 11 2021

Cảm ơn bạn ! ^^

18 tháng 12 2021

\(3,=\left(\dfrac{13}{25}-\dfrac{38}{25}\right)+\left(\dfrac{14}{9}-\dfrac{5}{9}\right)=-1+1=0\\ 4,=\left(\dfrac{4}{9}\right)^5\cdot\left(\dfrac{9}{49}\right)^5=\left(\dfrac{4}{9}\cdot\dfrac{9}{49}\right)^5=\left(\dfrac{4}{49}\right)^5\\ 5,\Rightarrow\dfrac{x}{5}=\dfrac{y}{3}=\dfrac{x-y}{5-3}=\dfrac{x+y}{5+3}=\dfrac{2}{2}=\dfrac{x+y}{8}\Rightarrow x+y=8\\ 6,\Rightarrow\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\Rightarrow2\text{ giá trị}\\ 7,=\dfrac{3^{10}\cdot2^{30}}{2^9\cdot3^9\cdot2^{20}}=2\cdot3=6\)

18 tháng 12 2021

Câu 7:

=6

21 tháng 7 2018

*Trả lời :

a) \(-\dfrac{3}{4}.5\dfrac{3}{13}-0,75.\dfrac{36}{13}\)

= \(-\dfrac{3}{4}.\dfrac{68}{13}-\dfrac{3}{4}.\dfrac{36}{13}\)

=\(\dfrac{3}{4}.\dfrac{-68}{13}-\dfrac{3}{4}.\dfrac{36}{13}\)

=\(\dfrac{3}{4}.\cdot\left(\dfrac{-68}{13}-\dfrac{36}{13}\right)\)

=\(\dfrac{3}{4}.\left(-8\right)\)

= \(-6\)

b)\(4\dfrac{5}{9}:\left(-\dfrac{5}{7}\right)+\dfrac{49}{9}:\left(-\dfrac{5}{7}\right)\)

=\(\dfrac{41}{9}-\left(-\dfrac{5}{7}\right)+\dfrac{49}{9}:\left(-\dfrac{5}{7}\right)\)

=\(\left(\dfrac{41}{9}+\dfrac{49}{9}\right):\left(-\dfrac{5}{7}\right)\)

=\(\dfrac{90}{9}:\left(-\dfrac{5}{7}\right)\)

=\(10:\left(-\dfrac{5}{7}\right)\)

=\(-14\)

c)\(\left(-\dfrac{3}{5}+\dfrac{4}{9}\right):\dfrac{7}{11}+\left(-\dfrac{2}{5}+\dfrac{5}{9}\right):\dfrac{7}{11}\)

=\(\left(-\dfrac{3}{5}\right)+\dfrac{4}{9}:\dfrac{7}{11}+\left(-\dfrac{2}{5}\right)+\dfrac{5}{9}:\dfrac{7}{11}\)(áp dụng tính chất phá ngoặc )

=\(\left\{\left[-\dfrac{3}{5}+\left(-\dfrac{2}{5}\right)\right]+\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\right\}:\dfrac{7}{11}\)

=\(\left(-\dfrac{5}{5}+\dfrac{9}{9}\right):\dfrac{7}{11}\)

=\(\left(-1+1\right):\dfrac{7}{11}\)

\(=0:\dfrac{7}{11}\)

=0.

d)\(\dfrac{6}{7}:\left(\dfrac{3}{26}-\dfrac{3}{13}\right)+\dfrac{6}{7}:\left(\dfrac{1}{10}-\dfrac{8}{5}\right)\)

=\(\dfrac{6}{7}:\left[\dfrac{3}{26}+\left(-\dfrac{6}{26}\right)\right]+\dfrac{6}{7}:\left[\dfrac{1}{10}+\left(-\dfrac{16}{10}\right)\right]\)

=\(\dfrac{6}{7}:\left(-\dfrac{3}{26}\right)+\dfrac{6}{7}:\left(-\dfrac{3}{2}\right)\)

=\(\dfrac{6}{7}:\left[\left(-\dfrac{3}{26}\right)+\left(-\dfrac{39}{26}\right)\right]\)

=\(\dfrac{6}{7}:\left(-\dfrac{21}{13}\right)\)

=\(-\dfrac{26}{49}\)

18 tháng 9 2023

a) \(=\left(13\dfrac{2}{7}+2\dfrac{5}{7}\right):\left(-\dfrac{8}{9}\right)\)

\(=16:\dfrac{-8}{9}=\dfrac{-8\cdot\left(-2\right)\cdot9}{-8}=-18\)

b) 

\(=\left(\dfrac{-6}{11}\cdot\dfrac{11}{-6}\right)\cdot\dfrac{7\cdot10\cdot\left(-2\right)}{10}\)

\(=-14\)

c) \(=\dfrac{-1}{2}\cdot\dfrac{4}{3}\cdot\dfrac{-7}{2}\)

\(=\dfrac{-1\cdot2\cdot2\cdot\left(-7\right)}{2\cdot3\cdot2}=\dfrac{7}{3}\)

20 tháng 12 2022

a: \(=\dfrac{3}{4}-\dfrac{5}{6}+\dfrac{3}{2}=\dfrac{9-10+18}{12}=\dfrac{17}{12}\)

b: \(=\left(\dfrac{1}{9}+\dfrac{6}{9}\right)^2-\dfrac{1}{3}=\dfrac{49}{81}-\dfrac{27}{81}=\dfrac{22}{81}\)

c; \(=\dfrac{5}{11}\left(-\dfrac{3}{7}-\dfrac{5}{7}\right)+\dfrac{-8}{7}\cdot\dfrac{6}{11}=\dfrac{-8}{7}\left(\dfrac{5}{11}+\dfrac{6}{11}\right)=-\dfrac{8}{7}\)

d: \(=\dfrac{2^{26}}{2^{15}\cdot2^{12}}=\dfrac{1}{2}\)

22 tháng 6 2022

a) A=35.67+37.35−27.35
=35⋅(67+37−27)=35
b) B=(−13⋅25+−29⋅25+25⋅119)⋅52
=(−13−29+119)⋅25⋅52=−13+(119−29)=−12.
c) C=(−45+57)⋅32+(−15+27)⋅32=(−45+57+−15+27)⋅32=((−45+−15)+(57+27))⋅32=0.
d) D=49:(115−1015)+49:(222−522)
=49:−35+49:−322=49⋅−53+49.−223

13 tháng 7 2022

a) \mathrm{A}=\dfrac{3}{5}. \dfrac{6}{7}+\dfrac{3}{7}. \dfrac{3}{5}-\dfrac{2}{7}. \dfrac{3}{5}

b)  \mathrm{B} =\left(-13 \cdot \dfrac{2}{5}+\dfrac{-2}{9} \cdot \dfrac{2}{5}+\dfrac{2}{5} \cdot \dfrac{11}{9}\right) \cdot \dfrac{5}{2}
=\left(-13-\dfrac{2}{9}+\dfrac{11}{9}\right) \cdot \dfrac{2}{5} \cdot \dfrac{5}{2}=-13+\left(\dfrac{11}{9}-\dfrac{2}{9}\right)=-12 .
c) \mathrm{C} =\left(\dfrac{-4}{5}+\dfrac{5}{7}\right) \cdot \dfrac{3}{2}+\left(\dfrac{-1}{5}+\dfrac{2}{7}\right) \cdot \dfrac{3}{2} =\left(\dfrac{-4}{5}+\dfrac{5}{7}+\dfrac{-1}{5}+\dfrac{2}{7}\right) \cdot \dfrac{3}{2}=\left(\left(\dfrac{-4}{5}+\dfrac{-1}{5}\right)+\left(\dfrac{5}{7}+\dfrac{2}{7}\right)\right) \cdot \dfrac{3}{2}=0 .
d) \mathrm{D}=\dfrac{4}{9}:\left(\dfrac{1}{15}-\dfrac{10}{15}\right)+\dfrac{4}{9}:\left(\dfrac{2}{22}-\dfrac{5}{22}\right)