![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
14/6 + 1/9 + 19/13 + 17/9 + 7/13 + 4/6 = (14/6 + 4/6) + (1/9 + 17/9) + (19/13 + 7/13)
= 18/6 + 18/9 + 26/13
= 3 + 2 + 2
= 7
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
$=(\frac{3}{5}+\frac{2}{5})+(\frac{5}{11}+\frac{16}{11})+(\frac{7}{13}+\frac{19}{13})$
$=\frac{5}{5}+\frac{22}{11}=\frac{26}{13}=1+2+2=5$
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
6 + 4 = (6 – 4)(6 + 4) = 210
Tương tự, 9 + 2 = (9 – 2)(9 + 2) = 711
Vì thế,
15 + 3 = (15 – 3)(15 + 3) = 1218
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{13\times15}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{13}-\frac{1}{15}\)
\(=\frac{1}{5}-\frac{1}{15}\)
\(=\frac{2}{15}\)
= 2 x (1/ 5 x 7 + 1/ 7 x 9 + ... + 1/ 13 x 15)
= 2 x (1/5 - 1/7 + 1/7 - 1/9 + ... + 1/13 - 1/15)
= 2 x (1/5 - 1/15)
= 2 x (3/15 - 1/15)
= 2 x 2/15
= 4/15
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\) (dấu chấm là dấu nhân)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=1-\frac{1}{7}\)
\(=\frac{6}{7}\)
b) \(\frac{19}{13}+\frac{14}{6}+\frac{1}{9}+\frac{4}{6}+\frac{7}{13}+\frac{17}{9}\)
\(=\left(\frac{19}{13}+\frac{7}{13}\right)+\left(\frac{14}{6}+\frac{4}{6}\right)+\left(\frac{1}{9}+\frac{17}{9}\right)\)
= 2 + 3 + 2
= 7
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{15}{8}:\dfrac{45}{6}-\dfrac{1}{13}\left(\dfrac{4}{9}-\dfrac{1}{12}\right)\)
\(=\dfrac{15}{8}\cdot\dfrac{6}{45}-\dfrac{1}{13}\left(\dfrac{48-9}{108}\right)\)
\(=\dfrac{1}{4}-\dfrac{1}{13}\cdot\dfrac{13}{36}\)
\(=\dfrac{1}{4}-\dfrac{1}{36}=\dfrac{2}{9}\)