Bài 6: So sánh phân số

\(\dfrac{5}{-6}=\dfrac{-55}{66};\dfrac{-10}{11}=\dfrac{-60}{66}\Rightarrow\dfrac{-55}{66}>\dfrac{-60}{66}\Rightarrow\dfrac{5}{-6}>\dfrac{-10}{11}\\ \dfrac{-3}{20}=\dfrac{-45}{300};\dfrac{2}{-15}=\dfrac{-40}{300}\Rightarrow\dfrac{-45}{300}< \dfrac{-40}{300}\Rightarrow\dfrac{-3}{20}< \dfrac{2}{-15}\\ -0,305>-0,36\)

\(^\circ\) \(\dfrac{5}{-6}\) và \(\dfrac{-10}{11}\)

Ta có \(:\)

\(\dfrac{5}{-6} = \dfrac{ 5 . 11 }{ -6 . 11 } = \dfrac{ 55 }{ -66} \)

\(\dfrac{-10}{11} = \dfrac{-10 . ( -6 )}{11.(-6)} = \dfrac{60}{-66}\)

Do \(55 < 60\)

\(=> \dfrac{55}{-66} > \dfrac{60}{-66}\)

Vậy \(\dfrac{55}{-66} > \dfrac{60}{-66}\)

\(\dfrac{-3}{20}\) và \(\dfrac{2}{-15}\)

Ta có :

\(\dfrac{-3}{20} = \dfrac{-3.3}{20.3}=\dfrac{-9}{60}\)

\(\dfrac{2}{-15} = \dfrac{2.4}{-15.4}= \dfrac{8}{-60}= \dfrac{-8}{60}\)

Do \(-9 <-8\)

\(=> \dfrac{-3}{20} < \dfrac{-2}{15}\)

Vậy \( \dfrac{-3}{20} < \dfrac{-2}{15}\)

A=1/2^2+1/3^2+...+1/100^2

=>A<1-1/2+1/2-1/3+...+1/99-1/100=99/100<1

1) \(16^{2020}+\dfrac{1}{16^{2021}}+1\)

\(=16^{2021}\div16^{2020}+1\)

\(=16+1\)

\(=17\)

2) \(16^{2021}+\dfrac{1}{16^{2022}}+1\)

\(=16^{2022}\div16^{2021}+1\)

\(=16+1\)

= 17

Vì 17=17 nên \(16^{2020}+\dfrac{1}{16^{2021}}+1=16^{2021}+\dfrac{1}{16^{2022}}+1\)

a: 18/31>18/36=1/2

15/37<15/30=1/2

=>18/31>15/37

\(A=\dfrac{10^{11}-1}{10^{12}-1}\\ 10A=\dfrac{10^{12}-10}{10^{12}-1}\\ 10A=1-\dfrac{9}{10^{12}-1}\\ \)

\(B=\dfrac{10^{10}+1}{10^{11}+1}\\ 10B=\dfrac{10^{11}+10}{10^{11}+1}\\ 10B=1+\dfrac{9}{10^{11}+1}\)

Vì `10^(11)+1<10^(12)-1` nên \(\dfrac{9}{10^{11}+1}>\dfrac{9}{10^{12}-1}\\ \Rightarrow1+\dfrac{9}{10^{11}+1}>1-\dfrac{9}{10^{12}-1}\\ \Rightarrow10B>10A\\ \Rightarrow B>A\)

a: \(\Leftrightarrow\dfrac{-3}{x-1}=\dfrac{y-2}{8}=\dfrac{-3}{4}\)

=>x-1=4; y-2=-6

=>x=5; y=-4

b: \(\Leftrightarrow5\left(x+5\right)=4\left(x-3\right)\)

=>5x+25=4x-12

=>x=-37

c: \(\Leftrightarrow\left(-\dfrac{3}{5}x-\dfrac{1}{2}\right)\cdot\dfrac{3}{4}=\dfrac{1}{3}-1=-\dfrac{2}{3}\)

\(\Leftrightarrow-\dfrac{3}{5}x-\dfrac{1}{2}=\dfrac{-2}{3}:\dfrac{3}{4}=\dfrac{-8}{9}\)

=>-3/5x=-7/18

hay x=35/54

\(\Leftrightarrow-\dfrac{3}{x-1}=\dfrac{y-2}{8}=\dfrac{-3}{4}\)

=>x-1=4 và y-2=-6

=>x=5 và y=-4

\(\dfrac{-7}{x}=\dfrac{-21}{x-34}\)

\(\Rightarrow-7\left(x-34\right)=-21x\)

\(-7x+238=-21x\)

\(-7x+21x=-238\)

14x=-238

x=-17

đk : x khác 0 ; 34

\(-7x+238=-21x\Leftrightarrow14x=-238\Leftrightarrow x=-17\)(tm) 

\(\Leftrightarrow\dfrac{-7\left(x-34\right)+21x}{x\left(x-34\right)}=0\\ \Leftrightarrow-7\left(x-34\right)+21x\\ \Leftrightarrow-7x+238+21x=0\\ \Leftrightarrow14x=-238\\ \Leftrightarrow x=-17\)