\(b,=-\dfrac{40}{30}-\dfrac{12}{30}-\dfrac{45}{30}=-\dfrac{97}{30}\\ c,=\left(\dfrac{4}{5}+\dfrac{7}{10}\right)+\dfrac{2}{7}=\dfrac{3}{2}+\dfrac{2}{7}=\dfrac{25}{14}\\ d,=\dfrac{2}{3}+\dfrac{7}{4}+\dfrac{1}{2}+\dfrac{3}{8}\\ =\left(\dfrac{2}{3}+\dfrac{1}{2}\right)+\left(\dfrac{7}{4}+\dfrac{3}{8}\right)=\dfrac{7}{6}+\dfrac{17}{8}=\dfrac{79}{24}\)

c: \(\dfrac{4}{5}-\dfrac{-2}{7}-\dfrac{-7}{10}\)

\(=\dfrac{56}{70}+\dfrac{20}{70}+\dfrac{49}{70}\)

\(=\dfrac{125}{70}=\dfrac{25}{14}\)

\(\dfrac{3}{7}.\left(\dfrac{13}{8}-\dfrac{7}{9}\right)-\dfrac{5}{8}.\left(\dfrac{3}{7}-\dfrac{8}{15}\right)\)

\(=\dfrac{3}{7}.\dfrac{13}{8}-\dfrac{3}{7}.\dfrac{7}{9}-\dfrac{5}{8}.\dfrac{3}{7}-\dfrac{5}{8}.\dfrac{8}{15}\)

\(=\dfrac{3}{7}.\left(\dfrac{13}{8}-\dfrac{5}{8}\right)-\dfrac{3.7}{7.9}-\dfrac{5.8}{8.15}\)

\(=\dfrac{3}{7}.\dfrac{8}{8}-\dfrac{1.1}{1.3}-\dfrac{1.1}{1.3}\)

\(=\dfrac{3}{7}.1-\dfrac{1}{3}-\dfrac{1}{3}\)

\(=\dfrac{3}{7}-\dfrac{1}{3}-\dfrac{1}{3}\)

\(=\dfrac{3}{7}-\left(\dfrac{1}{3}-\dfrac{1}{3}\right)\)

\(=\dfrac{3}{7}-0\)

\(=\dfrac{3}{7}\)

3/7 nha
chúc bạn học tốt

Ta có: \(\dfrac{3}{7}\left(\dfrac{13}{8}-\dfrac{7}{9}\right)-\dfrac{5}{8}\left(\dfrac{3}{7}-\dfrac{8}{15}\right)\)

\(=\dfrac{3}{7}\cdot\dfrac{13}{8}-\dfrac{1}{3}-\dfrac{3}{7}\cdot\dfrac{5}{8}+\dfrac{1}{5}\)

\(=\dfrac{3}{7}\)

a: \(\left(18\dfrac{1}{3}:\sqrt{225}+8\dfrac{2}{3}\cdot\sqrt{\dfrac{49}{4}}\right):\left[\left(12\dfrac{1}{3}+8\dfrac{6}{7}\right)-\dfrac{\left(\sqrt{7}\right)^2}{\left(3\sqrt{2}\right)^2}\right]:\dfrac{1704}{445}\)

\(=\left(\dfrac{55}{3}:15+\dfrac{26}{3}\cdot\dfrac{7}{4}\right):\left[\left(12+\dfrac{1}{3}+8+\dfrac{6}{7}\right)-\dfrac{7}{18}\right]\cdot\dfrac{445}{1704}\)

\(=\left(\dfrac{55}{45}+\dfrac{91}{6}\right):\left[20+\dfrac{101}{126}\right]\cdot\dfrac{445}{1704}\)

\(=\dfrac{295}{18}:\dfrac{2621}{126}\cdot\dfrac{445}{1704}\)

\(=\dfrac{295}{18}\cdot\dfrac{126}{2621}\cdot\dfrac{445}{1704}\simeq0,21\)

b: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{99\cdot100}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)

\(=1-\dfrac{1}{100}=\dfrac{99}{100}\)

c: \(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{n+1}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{n}{n+1}\)

\(=\dfrac{1}{n+1}\)

d: \(-66\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{11}\right)+124\cdot\left(-37\right)+63\cdot\left(-124\right)\)

\(=-66\cdot\dfrac{33-22+6}{66}+124\left(-37-63\right)\)

\(=-17-12400=-12417\)

e: \(\dfrac{7}{4}\left(\dfrac{33}{12}+\dfrac{3333}{2020}+\dfrac{333333}{303030}+\dfrac{33333333}{42424242}\right)\)

\(=\dfrac{7}{4}\left(\dfrac{33}{12}+\dfrac{33}{20}+\dfrac{33}{30}+\dfrac{33}{42}\right)\)

\(=\dfrac{7}{4}\cdot33\cdot\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\right)\)

\(=33\cdot\dfrac{7}{4}\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\right)\)

\(=33\cdot\dfrac{7}{4}\cdot\left(\dfrac{1}{3}-\dfrac{1}{7}\right)\)

\(=33\cdot\dfrac{7}{4}\cdot\dfrac{4}{21}=\dfrac{33\cdot1}{3}=11\)

Tính hợp lí: 

a) \(\left(-0,4\right)+\dfrac{3}{8}+\left(-0,6\right)\)

\(=\left[\left(-0,4\right)+\left(-0,6\right)\right]+\dfrac{3}{8}\)

\(=-1+\dfrac{3}{8}\)

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

\(=\dfrac{-5}{8}\)

b) \(\dfrac{4}{5}-1,8+0,375+\dfrac{5}{8}\)

\(=\dfrac{4}{5}-\dfrac{9}{5}+\dfrac{3}{8}+\dfrac{5}{8}\)

\(=-1+1\)

\(=0\\\)

c) \(\dfrac{7}{3}.\left(-2,5\right).\dfrac{6}{7}\)

\(=\dfrac{7}{3}.\dfrac{-5}{2}.\dfrac{6}{7}\)

\(=\dfrac{7}{3}.\dfrac{6}{7}.\dfrac{-5}{2}\)

\(=2.\dfrac{-5}{2}\)

\(=-5\)

d) \(\dfrac{7}{12}.\left(-2,34\right)-\dfrac{7}{12}.\left(-0,34\right)\)

\(=\dfrac{7}{12}.\left[\left(-2,34\right)+0,34\right]\)

\(=\dfrac{7}{12}.\left(-2\right)\)

\(=\dfrac{-7}{6}\)

e) \(\dfrac{-8}{3}.\dfrac{2}{11}-\dfrac{8}{3}:\dfrac{11}{9}\)

\(=\dfrac{8}{3}.\dfrac{-2}{11}-\dfrac{8}{3}.\dfrac{9}{11}\)

\(=\dfrac{8}{3}.\left(\dfrac{-2}{11}-\dfrac{9}{11}\right)\)

\(=\dfrac{8}{3}.-1\)

\(=\dfrac{-8}{3}\)

Chúc bạn học tốt

Cảm ơn nha.

a)\(\left(-0,4\right)+\dfrac{3}{8}+\left(-0,6\right)=\left(-\dfrac{4}{10}\right)+\dfrac{3}{8}+\left(-\dfrac{6}{10}\right)=-\dfrac{2}{5}+\dfrac{3}{8}-\dfrac{3}{5}=-\dfrac{2}{5}-\dfrac{3}{5}+\dfrac{3}{8}=-1+\dfrac{3}{8}=-\dfrac{5}{8}\)

b) \(\dfrac{4}{5}-1,8+0,375+\dfrac{5}{8}=\dfrac{4}{5}+\dfrac{5}{8}-1,425=\dfrac{57}{40}-\dfrac{1425}{1000}=\dfrac{57}{40}-\dfrac{57}{40}=0\)

c) \(\dfrac{7}{3}.\left(-2,5\right).\dfrac{6}{7}=\dfrac{7}{3}.\dfrac{6}{7}.\left(-\dfrac{25}{10}\right)=-5\)

d) \(\dfrac{7}{12}.\left(-2,34\right)-\dfrac{7}{12}.\left(-0,34\right)=\dfrac{7}{12}.\left(-2,34-0,34\right)=\dfrac{7}{12}.\left(-2,68\right)=\dfrac{7}{12}.\left(-\dfrac{268}{100}\right)=-\dfrac{7}{12}.\dfrac{4}{25}=-\dfrac{7}{75}\)

e) \(\dfrac{-8}{3}.\dfrac{2}{11}-\dfrac{8}{3}:\dfrac{11}{9}=-\dfrac{8}{3}.\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=-\dfrac{8}{3}.1=-\dfrac{8}{3}\)

ngu

Giải:

a)(-7/15-27/70)-(8/15+43/70)

=-7/15-27/70-8/15-43/70

=(-7/15-8/15)+(-27/70-43/70)

=-1+(-1)

=-2

b)3/7+(-1/5+-3/7)

=3/7-1/5+-3/7

=(3/7+-3/7)-1/5

=0-1/5

=-1/5

c)(4-12/5).25/8-2/5:-4/25

=8/5.25/8-(-5/2)

=5+5/2

=15/2

d)(-5/24+3/4-7/12):(-5/16)

=-1/24:(-5/16)

=2/15

e)-5/7.2/11+-5/7.9/11

=-5/7.(2/11+9/11)

=-5/7.1

=-5/7

g)6/7+5/4:(-5)-(-1/28).(-2)²

=6/7+(-1/4)-(-1/28).4

=6/7+(-1/4)-(-1/7)

=6/7-1/4+1/7

=(6/7+1/7)-1/4

=1-1/4

=3/4

Chúc bạn học tốt!

A -\(\dfrac{24}{25}\)

B -\(\dfrac{5}{21}\)

C -\(\dfrac{24}{47}\)

D -\(\dfrac{19}{42}\)

tick cho mk

6:ĐKXĐ: x>=0; x<>1/25

BPT=>\(\dfrac{3\sqrt{x}}{5\sqrt{x}-1}+3< =0\)

=>\(\dfrac{3\sqrt{x}+15\sqrt{x}-5}{5\sqrt{x}-1}< =0\)

=>\(\dfrac{18\sqrt{x}-5}{5\sqrt{x}-1}< =0\)

=>\(\dfrac{1}{5}< \sqrt{x}< =\dfrac{5}{18}\)

=>\(\dfrac{1}{25}< x< =\dfrac{25}{324}\)

7:

ĐKXĐ: x>=0

BPT \(\Leftrightarrow\dfrac{\sqrt{x}+1}{2\sqrt{x}+3}>\dfrac{8}{3}:\dfrac{8}{3}=1\)

=>\(\dfrac{\sqrt{x}+1}{2\sqrt{x}+3}-1>=0\)

=>\(\dfrac{\sqrt{x}+1-2\sqrt{x}-3}{2\sqrt{x}+3}>=0\)

=>\(-\sqrt{x}-2>=0\)(vô lý)

8:

ĐKXĐ: x>=0; x<>9/4

BPT \(\Leftrightarrow\dfrac{\sqrt{x}-2}{2\sqrt{x}-3}+4< 0\)

=>\(\dfrac{\sqrt{x}-2+8\sqrt{x}-12}{2\sqrt{x}-3}< 0\)

=>\(\dfrac{9\sqrt{x}-14}{2\sqrt{x}-3}< 0\)

TH1: 9căn x-14>0 và 2căn x-3<0

=>căn x>14/9 và căn x<3/2

=>14/9<căn x<3/2

=>196/81<x<9/4

TH2: 9căn x-14<0 và 2căn x-3>0

=>căn x>3/2 hoặc căn x<14/9

mà 3/2<14/9

nên trường hợp này Loại

9: 

ĐKXĐ: x>=0

\(BPT\Leftrightarrow\dfrac{2\sqrt{x}+3}{5\sqrt{x}+7}< =-\dfrac{1}{3}\)

=>\(\dfrac{2\sqrt{x}+3}{5\sqrt{x}+7}+\dfrac{1}{3}< =0\)

=>\(\dfrac{6\sqrt{x}+9+5\sqrt{x}+7}{3\left(5\sqrt{x}+7\right)}< =0\)

=>\(\dfrac{11\sqrt{x}+16}{3\left(5\sqrt{x}+7\right)}< =0\)(vô lý)

10: 

ĐKXĐ: x>=0; x<>1/49

\(BPT\Leftrightarrow\dfrac{6\sqrt{x}-2}{7\sqrt{x}-1}+6>0\)

=>\(\dfrac{6\sqrt{x}-2+42\sqrt{x}-6}{7\sqrt{x}-1}>0\)

=>\(\dfrac{48\sqrt{x}-8}{7\sqrt{x}-1}>0\)

=>\(\dfrac{6\sqrt{x}-1}{7\sqrt{x}-1}>0\)

TH1: 6căn x-1>0 và 7căn x-1>0

=>căn x>1/6 và căn x>1/7

=>căn x>1/6

=>x>1/36

TH2: 6căn x-1<0 và 7căn x-1<0

=>căn x<1/6 và căn x<1/7

=>căn x<1/7

=>0<=x<1/49

Lời giải:

a)

\(\frac{\frac{2}{3}-\frac{2}{5}+\frac{2}{7}-\frac{2}{9}+\frac{2}{11}}{\frac{8}{3}-\frac{8}{5}+\frac{8}{7}-\frac{8}{9}+\frac{8}{11}}=\frac{2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{7}-\frac{1}{9}+\frac{1}{11}\right)}{8\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{7}-\frac{1}{9}+\frac{1}{11}\right)}\) \(=\frac{2}{8}=\frac{1}{4}\)

b)

\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{50}-1\right)\left(\frac{1}{51}-1\right)\)

\(=\frac{1-2}{2}.\frac{1-3}{3}.\frac{1-4}{4}....\frac{1-50}{50}.\frac{1-51}{2}=\frac{(-1)(-2)(-3)...(-49)(-50)}{2.3.4....50.51}\)

\(=\frac{(-1)^{50}.1.2.3....49.50}{2.3.4...50.51}=\frac{1}{51}\)

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

Giúp mình với 

\(\left(8+\dfrac{9}{4}+\dfrac{2}{7}\right)-\left(-6-\dfrac{3}{7}+\dfrac{5}{4}\right)-\left(3+\dfrac{2}{4}-\dfrac{9}{7}\right)\)

\(=8+\dfrac{9}{4}+\dfrac{2}{7}+6+\dfrac{3}{7}-\dfrac{5}{4}-3-\dfrac{2}{4}+\dfrac{9}{7}\)

\(=11+\dfrac{1}{2}+2\)

\(=\dfrac{27}{2}\)