a) x⁴+x³+2x²+x+1=(x⁴+x³+x²)+(x²+x+1)=x²(x²+x+1)+(x²+x+1)=(x²+x+1)(x²+1)

b)a³+b³+c³-3abc=a³+3ab(a+b)+b³+c³ -(3ab(a+b)+3abc)=(a+b)³+c³-3ab(a+b+c)

=(a+b+c)((a+b)²-(a+b)c+c²)-3ab(a+b+c)=(a+b+c)(a²+2ab+b²-ac-ab+c²-3ab)=(a+b+c)(a²+b²+c²-ab-ac-bc)

c)Đặt x-y=a;y-z=b;z-x=c

a+b+c=x-y-z+z-x=o

đưa về như bài b

d)nhóm 2 hạng tử đầu lại và 2hangj tử sau lại để 2 hạng tử sau ở trong ngoặc sau đó áp dụng hằng đẳng thức dề tính sau đó dặt nhân tử chung

e)x²(y-z)+y²(z-x)+z²(x-y)=x²(y-z)-y²((y-z)+(x-y))+z²(x-y)

=x²(y-z)-y²(y-z)-y²(x-y)+z²(x-y)=(y-z)(x²-y²)-(x-y)(y²-z²)=(y-z)(x²-2y²+xy+xz+yz)

Dùng máy tính đấy em ơi

\(\frac{8}{9}+\frac{1}{3}=\frac{8}{9}+\frac{3}{9}=\frac{11}{9}\)

\(\frac{8}{9}+\frac{1}{3}=\frac{8}{9}+\frac{3}{9}=\frac{11}{9}\)

\(\frac{24}{15}-\frac{20}{25}=\frac{24}{15}-\frac{4}{5}=\frac{24}{15}-\frac{12}{15}=\frac{12}{15}\)

\(3\frac{1}{6}\times2\frac{3}{5}=\frac{19}{6}\times\frac{13}{5}=\frac{247}{30}\)

\(2\frac{1}{10}\div2\frac{2}{5}=\frac{21}{10}\div\frac{12}{5}=\frac{21}{10}\times\frac{5}{12}=\frac{7}{8}\)

a, 7/5 : x + 3/2 = 16/3

7/5 : x = 16/3 - 3/2

7/5 : x = 23/6

x = 7/5 : 23/6

x = 42/115

b, x : 1/5 + 1/7 = 3/5 . 18/21

x : 1/5 + 1/7 = 18/35

x : 1/5 = 18/35 - 1/7

x : 1/5 = 13/35

x = 13/35 . 1/5

x = 13/175

c, x - 1 và 1/3 : 2 = 5/7

x - 4/3 : 2 = 5/7

x - 4/3 = 5/7 . 2

x - 4/3 = 10/7

x = 10/7 + 4/3

x = 58/21

d, x + 2 và 3/5 . 1/6 = 35/36

x + 13/5 . 1/6 = 35/36

x + 13/5 = 35/36 : 1/6

x + 13/5 = 35/6

x = 35/6 - 13/5

x = 97/30

e, ( x + 3/2 ) : 2 = 7/10 + 1/5

( x + 3/2 ) : 2 = 9/10

x + 3/2 = 9/10 . 2

x + 3/2 = 9/5

x = 9/5 - 3/2

x = 3/10

10:5/3= 10x3/5=6

5/3:10=5/3x1/10=1/6

12/35:35/25=12/35x25/35=300/1225=12/49

19/17:76/51=19/17x 51/76= 3/4

\(10:\frac{5}{3}=10x\frac{3}{5}=\frac{30}{5}=6\)

\(\frac{5}{3}:10=\frac{5}{3}x\frac{1}{10}=\frac{5}{30}=\frac{1}{6}\)

\(\frac{12}{35}:\frac{35}{25}=\frac{12}{35}x\frac{25}{35}=\frac{12}{35}x\frac{5}{7}=\frac{12}{7}x\frac{1}{7}=\frac{12}{49}\)

\(\frac{19}{17}:\frac{76}{51}=\frac{19}{17}x\frac{51}{76}=\frac{1}{1}x\frac{3}{4}=\frac{3}{4}\)

Thank you! Chúc bạn học tốt!

bài 6 \(\frac{2}{2\times4}+\frac{2}{4\times6}+\frac{2}{6\times8}+\ldots+\frac{2}{80\times82}+\frac{2}{82\times84}\)

= \(\frac12-\frac14+\frac14-\frac16+\frac16-\cdots+\frac{1}{80}-\frac{1}{82}+\frac{1}{82}-\frac{1}{84}\)

= \(\frac12-\left(\frac14-\frac14\right)-\left(\frac16-\frac16\right)-\cdots-\left(\frac{1}{82}-\frac{1}{82}\right)-\frac{1}{84}\)

=\(\frac12-0-0-\frac{1}{84}\)

=\(\frac12\) - \(\frac{1}{84}\)

=\(\frac{42}{84}-\frac{1}{84}\)

=\(\frac{41}{84}\)

Bài 7

a)\(\frac{19}{4}=4\frac34\)

b)\(\frac{27}{5}=5\frac25\)

c)\(\frac{56}{8}=7\frac08\)

\(\frac{10}{18}+\frac{4}{9}+\frac{26}{10}+\frac{12}{5}+\frac{9}{15}\)

\(=\frac{5}{9}+\frac{4}{9}+\frac{13}{5}+\frac{12}{5}+\frac{3}{5}\)

\(=\left(\frac{5}{9}+\frac{4}{9}\right)+\left(\frac{13}{5}+\frac{12}{5}+\frac{3}{5}\right)\)

\(=1+\frac{28}{5}\)

\(=\frac{33}{5}\)

Ta có:

a) \(\frac{10}{18}+\frac{4}{9}+\frac{26}{10}+\frac{12}{5}+\frac{9}{15}=\frac{5}{9}+\frac{4}{9}+\frac{13}{5}+\frac{12}{5}+\frac{9}{15}=1+1+\frac{9}{15}=1\frac{9}{15}\)

b)\(\frac{10}{18}+\frac{4}{9}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}=\left(\frac{5}{9}+\frac{4}{9}\right)+\left(\frac{16}{128}+\frac{8}{128}+\frac{4}{128}+\frac{2}{128}+\frac{1}{128}\right)\)

\(=1+\frac{31}{128}=1\frac{31}{128}\)

Bài 1 : 

a) \(\frac{6}{10}\)

Bài 2 :

c) \(\frac{8}{18}\)

Bài 1:

Kết quả:\(\frac{6}{10}\)

Bài 2:

Kết quả:\(\frac{8}{18}\)

                                                                                           K CHO MK NHA:   

                                                                                                  KÍ TÊN

                                                                              \(!@#HUYDEPZAI\%\&\)

\(\frac{12}{35}:\frac{35}{25}=\frac{12}{35}.\frac{25}{35}=\frac{12.25}{35.35}=\frac{12.5.5}{7.5.7.5}=\frac{12}{49}\)

\(\frac{9}{22}.\frac{33}{18}=\frac{9.33}{22.18}=\frac{9.3.11}{11.2.9.2}=\frac{3}{4}\)