a: 90/126=5/7<6/7

b: 70/84=5/6

35/42=5/6

=>70/84=35/42

a)\(\dfrac{90}{126}=\dfrac{5}{7}< \dfrac{6}{7}\Leftrightarrow\cdot\dfrac{90}{126}< \dfrac{6}{7}\)

b)\(\dfrac{70}{84}=\dfrac{5}{6};\dfrac{35}{42}=\dfrac{5}{6}\Leftrightarrow\cdot\dfrac{70}{84}=\dfrac{35}{42}\)

a: 34/56=17/28=1-11/28

42/53=1-11/53

mà 11/28>11/53

nên 34/56<42/53

b: 5/4=15/12; 7/6=14/12; 5/6=10/12

=>5/4>7/6>5/6

c: 4/3>1>99/100

\(-\frac{3}{7}.\frac{5}{9}+\frac{4}{9}.\frac{-3}{7}+2.\frac{3}{7}\)\(=\frac{3}{7}\left(-\frac{5}{9}-\frac{4}{9}+2\right)=\frac{3}{7}\left(-1+2\right)=\frac{3}{7}\)

so sánh: \(\frac{21}{-42}=\frac{1}{-2}=\frac{2}{-4}\); vì \(\frac{2}{-4}>\frac{3}{-4}\)nên \(\frac{21}{-42}>\frac{3}{-4}\)

tìm x: a) \(x-\frac{2}{5}=\frac{1}{10}\)

             \(\Rightarrow x=\frac{1}{10}+\frac{2}{5}=\frac{1}{10}+\frac{4}{10}=\frac{5}{10}=\frac{1}{2}\)

b) \(\frac{4}{6}+\frac{5}{4}x=\frac{7}{6}\)

\(\Rightarrow\frac{5}{4}x=\frac{3}{6}=\frac{1}{2}\)

\(\Rightarrow x=\frac{2}{5}\)

\(a.\frac{1}{2}+\frac{7}{8}+\frac{17}{19}+\frac{42}{47}< 1+1+1+1\)

                                              \(< 4\)

\(b.\frac{3}{2}+\frac{6}{5}+\frac{17}{11}+\frac{197}{193}>1+1+1+1\)

                                                \(>4\)

Ủng hộ mk nha ^_-

a)Ta có:

1/2<1                     7/8<1                 17/19<1                    42/47<1

Vậy:

1/2+7/8+17/19+42/47<1+1+1+1(do từng số hạng trong vế trái đều nhỏ hơn từng số hạng bên vế phải)

Vậy: 1/2+7/8+17/19+42/47<4

b)Ta có:

3/2>1         6/5>1                   17/11>1                   197/193>1

Vậy:

3/2+6/5+17/11+197/193>1+1+1+1

Vậy 3/2+6/5+17/11+197/193>4

Chúc em học tốt^^

\(7^{28}=\left(7^2\right)^{14}=49^{14}\)

\(5^{42}=\left(5^3\right)^{14}=125^{14}\)

Vì 49 < 125 và 14 = 14 

=> \(49^{14}< 125^{14}\)

=> \(7^{28}< 5^{42}\)

Ta có:7²⁸=(7²)¹⁴=49¹⁴

5⁴²=(5³)¹⁴=125¹⁴

Vì 125¹⁴>49¹⁴ nên 5⁴²>7²⁸

suy ra : (7^4)^7=2402^7

(5^6)^7=15625^7

vì 2402^7<15625^7 suy ra 7^28<5^42

Ta co:

1/2+1/6+1/12+1/20+1/30+1/42

=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

=1-1/7

=6/7

Ta co: 6/7=6.10101/7.10101=60606/70707 

Vi 60606/70707=60606/70707 nen 6/7=60606/70707

Vay 1/2+1/6+1/12+1/20+1/30+1/42 = 60606/70707

ta có:

\(\frac{60606}{70707}=\frac{6}{7}\)

ta có:

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}=\)

\(1-\frac{1}{2}+\frac{1}{2}-...-\frac{1}{7}=\frac{6}{7}\)

suy ra 6/7=6/7

suy ra \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}=\frac{60606}{70707}\)

B<A