A = \(\frac{1}{5\times6}+\frac{3}{6\times9}+\frac{5}{9\times14}+\frac{7}{14\times21}+\frac{9}{21\times30}\)

A = \(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{21}+\frac{1}{21}-\frac{1}{30}\)

A = \(1-\frac{1}{30}\)

A = \(\frac{29}{30}\)

a, 5/-14. 7/-19=8/38

b, -15/4 .( 16/-25 )=12/5

c, 3/-10 .( -15/-2 )=

d, -5/7 . ( 21/-10 )=-9/4

e, 10/-3. (6/-5)==4

f, 21/-9 . ( -6/14 )=1

g, -10/9 . ( 36/20 )=-2

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Nhanh rồi mình tích cho

a: \(\dfrac{6}{7}\cdot\dfrac{16}{15}\cdot\dfrac{7}{6}\cdot\dfrac{21}{32}=\dfrac{16}{32}\cdot\dfrac{21}{15}=\dfrac{1}{2}\cdot\dfrac{7}{5}=\dfrac{7}{10}\)

b: \(\dfrac{21}{17}\cdot\dfrac{13}{14}\cdot56\cdot\dfrac{3}{42}=\dfrac{21}{14}\cdot\dfrac{13}{17}\cdot\dfrac{1}{14}\cdot56=\dfrac{78}{17}\)

c: \(=\dfrac{11}{21}\left(\dfrac{7}{4}+\dfrac{5}{4}\right)=\dfrac{11}{21}\cdot3=\dfrac{11}{7}\)

1)1/6 - - 5/6 = 1/6 + 5/6 = 1

2)6/13 - -14/39 = 6/13 + 14/39= 32/39

3)4/5 - 4/-18 = 4/5 + 4/18= 46/45

4)7/21 - 9/-36 = 7/21 + 9/36 = 7/12

5)-12/18 - -21/35  = -12/18 + 21/35 = -1/15

6)-3/21 - 6/42 = -2/7

7)-18/24 - 15/21 = -41/28

8)1/6 - 2/5 =-7/30

Lời giải:
Đặt biểu thức là $A$. Ta có:

\(A=(5+\sqrt{21})(\sqrt{7}-\sqrt{3}).\sqrt{2}.\sqrt{5-\sqrt{21}}\)

\(=(5+\sqrt{21})(\sqrt{7}-\sqrt{3}).\sqrt{10-2\sqrt{21}}\)

\(=(5+\sqrt{21})(\sqrt{7}-\sqrt{3}).\sqrt{(\sqrt{7}-\sqrt{3})^2}\)

\(=(5+\sqrt{21})(\sqrt{7}-\sqrt{3})|\sqrt{7}-\sqrt{3}|=(5+\sqrt{21})(\sqrt{7}-\sqrt{3})^2\)

\(=(5+\sqrt{21})(10-2\sqrt{21})=2(5+\sqrt{21})(5-\sqrt{21})=2(5^2-21)=8\)

Ta có: \(\left(5+\sqrt{21}\right)\cdot\left(\sqrt{14}-\sqrt{6}\right)\cdot\sqrt{5-\sqrt{21}}\)

\(=\dfrac{\left(10+2\sqrt{21}\right)\cdot\left(\sqrt{7}-\sqrt{3}\right)\cdot\sqrt{10-2\sqrt{21}}}{2}\)

\(=\dfrac{\left(\sqrt{7}+\sqrt{3}\right)^2\cdot\left(\sqrt{7}-\sqrt{3}\right)^2}{2}\)

=8

\(\frac{7}{8}\div\left(\frac{14}{3}+\frac{14}{4}\right)+\frac{10}{14}\)

\(=\frac{7}{8}\div\left(\frac{56}{12}+\frac{52}{12}\right)+\frac{10}{14}\)

\(=\frac{7}{8}\div\frac{108}{12}+\frac{10}{14}\)

\(=\frac{7}{8}\div9+\frac{5}{7}\)

\(=\frac{7}{8}\times\frac{1}{9}+\frac{5}{7}\)

\(=\frac{7}{72}+\frac{5}{7}\)

\(=\frac{49}{504}+\frac{360}{504}\)

\(=\frac{409}{504}\)

\(\frac{30}{42}\div\left(\frac{5}{7}-\frac{5}{21}\right)+\frac{6}{8}\)

\(=\frac{6}{7}\div\left(\frac{15}{21}-\frac{5}{21}\right)+\frac{3}{4}\)

\(=\frac{6}{7}\div\frac{10}{21}+\frac{3}{4}\)

\(=\frac{6}{7}\times\frac{21}{10}+\frac{3}{4}\)

\(=\frac{126}{70}+\frac{3}{4}\)

\(=\frac{504}{280}+\frac{210}{280}\)

\(=\frac{714}{280}\)

\(\left(6-\frac{14}{15}\right).\frac{50}{38}-\frac{8}{18}\)

\(=\left(\frac{90}{15}-\frac{14}{15}\right).\frac{25}{19}-\frac{4}{9}\)

\(=\frac{76}{15}.\frac{25}{19}-\frac{4}{9}\)

\(=\frac{76.25}{15.19}-\frac{4}{9}\)

\(=\frac{19.2.2.5.5}{3.5.19}-\frac{4}{9}\)

\(=\frac{20}{3}-\frac{4}{9}\)

\(=\frac{60}{9}-\frac{4}{9}\)

\(=\frac{56}{9}\)

\(\frac{4}{6}+\frac{5}{21}.\left(\frac{4}{5}-\frac{2}{6}\right)\)

\(=\frac{2}{3}+\frac{5}{21}.\left(\frac{24}{30}-\frac{10}{30}\right)\)

\(=\frac{2}{3}+\frac{5}{21}.\frac{14}{30}\)

\(=\frac{2}{3}+\frac{70}{630}\)

\(=\frac{420}{630}+\frac{70}{630}\)

\(=\frac{490}{630}\)

\(=\frac{7}{9}\)

\(\left(6-\frac{4}{15}\right).\frac{25}{8}-\frac{18}{5}:\frac{1}{4}\)

\(=\frac{86}{15}.\frac{25}{8}-\frac{72}{5}\)

\(=\frac{215}{12}-\frac{72}{5}\)

\(=\frac{211}{60}\)

\(\frac{5}{6}:7:\frac{20}{11}+\frac{5}{6}:7:\frac{20}{11}\)

\(=\frac{11}{168}+\frac{11}{168}\)

\(=\frac{11}{84}\)

học tốt

ví dụ 1 bài 2x-x²

bài giải: -(x²+2x)

=-(x²-2x)

=-(x²-2x.5/2 +25/4 - 25/4)

=-(x-5/2)-25/4<25/4

=25/4+(x-5/2)<25

=>x=5/2

Tìm GTLN của biểu thức: a,A= (21|4x+6| + 33)/(3|4x+6|+5)