Lời giải:

$8b-9a=31\Rightarrow a=\frac{8b-31}{9}$

$\frac{a}{b}> \frac{14}{17}$

$\Rightarrow 17a-14b>0$

$\Rightarrow 17.\frac{8b-31}{9}-14b>0$

$\Rightarrow 17(8b-31)-126b>0$

$\Rightarrow 10b> 527\Rightarrow b> 52,7(1)$

Lại có:

$\frac{a}{b}< \frac{23}{29}$

$\Rightarrow 29a-23b<0$

$\Rightarrow 29.\frac{8b-31}{9}-23b<0$

$\Rightarrow 29(8b-31)-207b<0$

$\Rightarrow 25b< 899$

$\Rightarrow b< 35,96(2)$

Từ $(1); (2)\Rightarrow 52,7< 35,96$ (vô lý)

Bạn xem lại đề.

Lời giải:

Ta có:

\(\frac{x-2}{5}=\frac{1-x}{6}\)

$\Rightarrow 6(x-2)=5(1-x)$

$\Rightarrow 6x-12=5-5x$

$\Rightarrow 11x=17$

$\Rightarrow x=\frac{17}{11}$

400

400 cm²

Bằng 107.3

=107.3

Bạn cần viết đầy đủ yêu cầu đề để được hỗ trợ tốt hơn nhé.

a/\(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{37.39}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{37}-\dfrac{1}{39}\)
\(=\dfrac{1}{3}-\dfrac{1}{39}\)
\(=\dfrac{4}{13}\)

6.1

\(\frac{3}{8}-\frac{4}{5}-\frac{-17}{40}=\frac{15}{40}-\frac{32}{40}+\frac{17}{40}=\frac{15+17-32}{40}=0\)

6.2

\(\frac{3}{4}-\frac{16}{32}+\frac{4}{-3}=\frac{9}{12}-\frac{6}{12}-\frac{16}{12}=\frac{9-6-16}{12}=\frac{-13}{12}\)

6.3

\(\frac{-4}{7}+\frac{2}{3}.\frac{-9}{14}=\frac{-4}{7}-\frac{3}{7}=-\frac{7}{7}=-1\)

6.4

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

6.5

\((\frac{2}{3}-1\frac{1}{2}):\frac{4}{3}+\frac{1}{2}=\frac{-5}{6}.\frac{3}{4}+\frac{1}{2}=\frac{-5}{8}+\frac{1}{2}=\frac{-5}{8}+\frac{4}{8}=\frac{-1}{8}\)

6.6

\(\frac{-5}{13}+\frac{2}{5}+\frac{-8}{13}+\frac{3}{5}-\frac{3}{7}\\ =(\frac{-5}{13}+\frac{-8}{13})+(\frac{2}{5}+\frac{3}{5})-\frac{3}{7}\\ =-1+1-\frac{3}{7}=\frac{-3}{7}\)

Bài 8:

a/ $=(\frac{2}{3}-\frac{2}{3})+\frac{5}{7}=0+\frac{5}{7}=\frac{5}{7}$

b/ $=(\frac{5}{13}+\frac{8}{13})+\frac{-5}{7}+(\frac{-20}{41}+\frac{-21}{41})$

$=1-\frac{5}{7}-1=-\frac{5}{7}$

c/ $=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}$

$=\frac{1}{2}(\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+\frac{11-9}{9.11}+\frac{13-11}{11.13})$

$=\frac{1}{2}(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13})$

$=\frac{1}{2}(\frac{1}{3}-\frac{1}{13})$

$=\frac{5}{39}$

Đề không đủ dữ kiện để tính toán. Bạn xem lại.

b/

$\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{2}{x(x+1)}=\frac{2021}{2022}$

$\Rightarrow \frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{x(x+1)}=\frac{2021}{2022}$

$\Rightarrow 2(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{x+1-x}{x(x+1)})=\frac{2021}{2022}$

$\Rightarrow 2(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1})=\frac{2021}{2022}$

$\Rightarrow 2(\frac{1}{2}-\frac{1}{x+1})=\frac{2021}{2022}$

$\Rightarrow 1-\frac{2}{x+1}=\frac{2021}{2022}$

$\Rightarrow \frac{2}{x+1}=\frac{1}{2022}$

$\Rightarrow x+1=4044$
$\Rightarrow x=4043$

Lời giải:

a/

$(x+\frac{4}{1}-\frac{1}{3}):(2+\frac{1}{6}-\frac{1}{4})=\frac{7}{46}$

$(x+\frac{11}{3}):\frac{23}{12}=\frac{7}{46}$

$x+\frac{11}{3}=\frac{7}{46}.\frac{23}{12}=\frac{7}{24}$

$x=\frac{7}{24}-\frac{11}{3}=\frac{-27}{8}$