\(\dfrac{1}{5}:\left(x-3\right)+\dfrac{1}{2}=1\dfrac{1}{8}\\ \Rightarrow\dfrac{1}{5}:\left(x-3\right)=\dfrac{9}{8}-\dfrac{1}{2}\\ \Rightarrow\dfrac{1}{5}:\left(x-3\right)=\dfrac{9}{8}-\dfrac{4}{8}\\ \Rightarrow\dfrac{1}{5}:\left(x-3\right)=\dfrac{5}{8}\\ \Rightarrow x-3=\dfrac{1}{5}:\dfrac{5}{8}\\ \Rightarrow x-3=\dfrac{8}{25}\\ \Rightarrow x=\dfrac{8}{25}+3\\ \Rightarrow x=\dfrac{83}{25}\)

\(\dfrac{1}{5}:\left(x-3\right)+\dfrac{1}{2}=1\dfrac{1}{8}\)

\(\dfrac{1}{5}:\left(x-3\right)+\dfrac{1}{2}=\dfrac{9}{8}\)

\(\dfrac{1}{5}:\left(x-3\right)=\dfrac{9}{8}-\dfrac{1}{2}=\dfrac{9}{8}-\dfrac{4}{8}\)

\(\dfrac{1}{5}:\left(x-3\right)=\dfrac{5}{8}\)

\(x-3=\dfrac{1}{5}:\dfrac{5}{8}=\dfrac{1}{5}.\dfrac{8}{5}\)

\(x-3=\dfrac{8}{25}\)

\(x=\dfrac{8}{25}+3=\dfrac{8}{25}+\dfrac{75}{25}\)

\(x=\dfrac{83}{25}\)

Nghiệm của đa thức trên là: x = 9

Ngiệm là 9 nha

\(\dfrac{2}{9}\cdot\dfrac{5}{17}+\dfrac{2}{9}\cdot\dfrac{12}{17}-\dfrac{1}{9}\\ \\ \\ =\dfrac{2}{9}\cdot\left(\dfrac{5}{17}+\dfrac{12}{17}\right)-\dfrac{1}{9}\\ \\ \\ =\dfrac{2}{9}\cdot1-\dfrac{1}{9}\\ \\ \\ =\dfrac{2}{9}-\dfrac{1}{9}=\dfrac{1}{9}\)

Bạn ơi 12/7 chứ ko phải 12/17 đâu nhé

a) \(\dfrac{2}{1\times4}+\dfrac{2}{4\times7}+\dfrac{2}{7\times10}+...+\dfrac{2}{97\times100}\)

\(=2.\left(\dfrac{1}{1\times4}+\dfrac{1}{4\times7}+\dfrac{1}{7\times10}+...+\dfrac{1}{97\times100}\right)\)

\(=2.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(=2.\left(1-\dfrac{1}{100}\right)\)

\(=2.\dfrac{99}{100}\)

\(=\dfrac{99}{50}\)

_____

b) \(\dfrac{3}{1\times5}+\dfrac{3}{5\times9}+\dfrac{3}{9\times13}+...+\dfrac{3}{97\times101}\)

\(=3.\left(\dfrac{1}{1\times5}+\dfrac{1}{5\times9}+\dfrac{1}{9\times13}+...+\dfrac{1}{97\times101}\right)\)

\(=3.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{97}-\dfrac{1}{101}\right)\)

\(=3.\left(1-\dfrac{1}{101}\right)\)

\(=3.\dfrac{100}{101}\)

\(=\dfrac{300}{101}\)

dấu " . "  là dấu nhân nha bn, nãy viết nhanh quên lớp 

a) \(12\dfrac{1}{3}-\left(3\dfrac{3}{4}+4\dfrac{3}{4}\right)=\dfrac{37}{3}-\left(\dfrac{15}{4}+\dfrac{19}{4}\right)\)

\(=\dfrac{37}{3}-\dfrac{34}{4}=\dfrac{37}{3}-\dfrac{17}{2}=\dfrac{74}{6}-\dfrac{51}{6}=\dfrac{23}{6}\)

b) \(3\dfrac{5}{6}+2\dfrac{1}{6}.6=\dfrac{23}{6}+\dfrac{13}{6}.6=\dfrac{23}{6}+\dfrac{78}{6}=\dfrac{101}{6}\)

c) \(3\dfrac{1}{2}+4\dfrac{5}{7}-5\dfrac{5}{14}=\dfrac{7}{2}+\dfrac{33}{7}-\dfrac{75}{14}=\dfrac{49}{14}+\dfrac{66}{14}-\dfrac{75}{14}=-\dfrac{92}{14}=-\dfrac{46}{7}\)

d) \(4\dfrac{1}{2}+\dfrac{1}{2}:5\dfrac{1}{2}=\dfrac{9}{2}+\dfrac{1}{2}:\dfrac{11}{2}=\dfrac{9}{2}+\dfrac{1}{2}.\dfrac{2}{11}=\dfrac{9}{2}+\dfrac{1}{11}=\dfrac{99}{22}+\dfrac{2}{22}=\dfrac{101}{22}\)

a. \(12\dfrac{1}{3}-\left(3\dfrac{3}{4}+4\dfrac{3}{4}\right)=\dfrac{37}{3}-\left(\dfrac{15}{4}+\dfrac{19}{4}\right)\)

\(=\dfrac{37}{3}-\dfrac{34}{4}=\dfrac{23}{6}\)

\(b.3\dfrac{5}{6}+2\dfrac{1}{6}.6=\dfrac{23}{6}+13=\dfrac{101}{6}\)

\(c.3\dfrac{1}{2}+4\dfrac{5}{7}-5\dfrac{5}{14}=\dfrac{7}{2}+\dfrac{33}{7}-\dfrac{75}{14}=\dfrac{20}{7}\)

d  \(4\dfrac{1}{2}+\dfrac{1}{2}:5\dfrac{1}{2}\)

\(=\dfrac{9}{2}+\dfrac{1}{2}:\dfrac{11}{2}\)

\(=\dfrac{9}{2}+\dfrac{1}{11}\)

\(=\dfrac{101}{22}\)

a. \(\dfrac{2021+2020.2022}{2021.2022-1}\)

\(\dfrac{2021.2022-2022+2021}{2021.2022-1}=\dfrac{2021.2022-1}{2021.2022-1}=1\)

\(b.\dfrac{2022+2021.2023}{2022.2023-1}=\dfrac{2021.2023-2023+2022}{2022.2023-1}\)

\(=\dfrac{2021.2023-1}{2022.2023-1}\)

thanks các cậu nhiều

a/

\(10^{33}⋮2;8⋮2\Rightarrow\left(10^{33}+8\right)⋮2\)

\(10^{33}+8=999...99+1+8=999...99+9\) (33 chữ số 9)

\(999...99+9⋮9\Rightarrow\left(10^{33}+8\right)⋮9\)

Mà 2 và 9 là 2 số nguyên tố cùng nhau

\(\Rightarrow\left(10^{33}+8\right)⋮2x9\Rightarrow\left(10^{33}+8\right)⋮18\)

b/

\(10^{10}⋮2;14⋮2\Rightarrow\left(10^{10}+14\right)⋮2\)

\(10^{10}+14=999..99+1+14=999...99+15⋮3\) (10 chữ số 9)

\(\Rightarrow\left(10^{10}+14\right)⋮3\)

2 và 3 là 2 số nguyên tố cùng nhau

\(\Rightarrow\left(10^{10}+14\right)⋮2x3\Rightarrow\left(10^{10}+14\right)⋮6\)

a) (10³³ +8) ⋮ 18

=> Ta phải CM được (10³³ +8) ⋮ 2; (10³³ +8) ⋮ 9

+) 10³³ +8 = \(\overline{...0}+8=\overline{........8}\)

Vì (10³³ +8)  có chữ số tận cùng là chẵn => (10³³ +8) ⋮ 2

+) (10³³ +8) có tổng các chữ số = 9 =>  (10³³ +8) ⋮ 9

CMR: (10³³ +8) ⋮ 18

b) (10¹⁰ + 14) ⋮ 6

=> Ta phải Cm được (10¹⁰ + 14) ⋮2 ;(10¹⁰ + 14) ⋮ 3

+) (10¹⁰ + 14) = \(\overline{......00}+14=\overline{..........14}\)

Vì (10¹⁰ + 14) có chữ số tận cùng là số chẵn => (10¹⁰ + 14) ⋮ 2

+) Vì (10¹⁰ + 14) có tổng các chữ số = 6 => (10¹⁰ + 14) ⋮ 3

đã CMR: (10¹⁰ + 14) ⋮6

a,với y=0 thì x=1,4,7

b,với b=0 thì a=1,9

với b=4 thì a=5

với b=8 thì a=2

GT:a, vì số 48x5y chia hết cho 2 và 5 nên y=0

⇒4+8+x+5+0⋮3

⇒17⋮3

⇒.......

b, phân tích 36 thành 4 và 9 và làm tuoưng tự câu a

Bạn xem lại đề bài

\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{2a}{2b}=\dfrac{3c}{3d}=\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)

\(\Rightarrow\dfrac{2a+3c}{2a-3c}=\dfrac{2b+3d}{2b-3d}\)

\(\Rightarrow dpcm\)