\(\dfrac{7}{4}.\dfrac{29}{5}-\dfrac{7}{5}.\dfrac{9}{4}+3\dfrac{2}{15}\)         (đổi hỗn số ra phân số)

\(=\) \(\dfrac{7}{4}.\dfrac{29}{5}-\dfrac{7}{5}.\dfrac{9}{4}+\dfrac{47}{15}\)       (nhân, chia trước cộng, trừ sau lấy \(\dfrac{7}{4}.\dfrac{29}{5}\)và lấy \(\dfrac{7}{5}.\dfrac{9}{4}\) ra kết quả rồi \(+\dfrac{47}{15}\))

\(=\dfrac{203}{20}-\dfrac{63}{20}+\dfrac{47}{15}\)             (cộng, trừ thì cộng, trừ từ trái sang phải)

\(=7+\dfrac{47}{15}=\dfrac{7}{1}+\dfrac{47}{15}\)

\(=\dfrac{105}{15}+\dfrac{47}{15}\)

\(=\dfrac{152}{15}\)

NHỮNG CHỮ IN ĐẬM BẠN KHÔNG CẦN GHI 

\(\left(-\dfrac{2}{3}+\dfrac{3}{7}\right):\dfrac{4}{5}+\left(-\dfrac{1}{3}+\dfrac{4}{7}\right)+\dfrac{4}{5}\\ =-\dfrac{5}{21}:\dfrac{4}{5}+\dfrac{5}{21}\\ =\left(-\dfrac{5}{21}+\dfrac{5}{21}\right):\dfrac{4}{5}\\ =0:\dfrac{4}{5}\\ =0.\)

Sửa cho mk dòng đầu là :4/5 và dòng tiếp theo mk thiếu :4/5

viết đề sai kìa bạn tui ới.

e) \(\left(\dfrac{-1}{3}\right)\cdot\dfrac{5}{7}=\dfrac{\left(-1\right)\cdot5}{3\cdot7}=\dfrac{-5}{21}\)

f) \(\dfrac{2}{7}:\dfrac{3}{4}=\dfrac{2}{7}\cdot\dfrac{4}{3}=\dfrac{8}{21}\)

\(e.\left(\dfrac{-1}{3}\right).\dfrac{5}{7}=\dfrac{\left(-1\right).5}{3.7}=\dfrac{-5}{21}\\ f.\dfrac{2}{7}:\dfrac{3}{4}=\dfrac{2}{7}.\dfrac{4}{3}=\dfrac{2.4}{7.3}=\dfrac{8}{21}\)

\(\dfrac{2}{7}x=\dfrac{4}{15}+\dfrac{3}{5}\)

\(\dfrac{2}{7}x=\dfrac{13}{15}\)

\(x=\dfrac{13}{15}:\dfrac{2}{7}\)

\(x=\dfrac{13}{15}x\dfrac{7}{2}\)

\(x=\dfrac{91}{30}\)

     \(\dfrac{2}{7}x-\dfrac{3}{5}=\dfrac{4}{15}\)

⇔ \(\dfrac{2}{7}x=\dfrac{4}{15}+\dfrac{3}{5}\)

⇔\(\dfrac{2}{7}x=\dfrac{13}{15}\)

⇔\(x=\dfrac{13}{15}:\dfrac{2}{7}\)

⇔\(x=\dfrac{91}{30}\)

\(\frac{4}{7}+x\times2=\frac{5}{3}\)

           \(x\times2=\frac{5}{3}-\frac{4}{7}\)

           \(x\times2=\frac{23}{21}\)

                    \(x=\frac{23}{21}:2\) 

                     \(x=\frac{23}{42}\)

\(\frac{4}{7}+x\times2=\frac{5}{3}\)

          \(x\times2=\frac{5}{3}-\frac{4}{7}\)

           \(x\times2=\frac{23}{21}\)

                   \(x=\frac{23}{21}:2\)

                   \(x=\frac{23}{42}\)

Vậy x = 23/42

x*2=5/3-4/7

x*2=23/21

x   =23/21:2

x   =23/42

-5/6:-3/4;7/24;2/3;7/8;16/17 

-5/6 , -3/4 , 7/24 , 2/3 , 7/8 , 16/17

4/7 *1/3+5/7:2/3

\(\frac{4}{21}\)+ \(\frac{15}{14}\)= \(\frac{53}{42}\)

=4/21+15/14

=53/42

cho hỏi 4/21,15/14 đâu ra vậy,hai bạn làm ko đúng,sao có người làm bằng 1 vậy

5/8

3/4

\(a)\dfrac{3}{4}.\dfrac{5}{6}=\dfrac{5}{8}\)

\(b)\dfrac{2}{7}:\dfrac{4}{9}=\dfrac{9}{14}\)

\(\dfrac{3}{4}x\dfrac{5}{6}=\dfrac{3x5}{4x6}=\dfrac{15}{24}=\dfrac{5}{8}\)

b) \(\dfrac{2}{7}:\dfrac{4}{9}=\dfrac{2}{7}x\dfrac{9}{4}=\dfrac{18}{28}=\dfrac{9}{14}\)

\(\sqrt{13+\sqrt{48}}=\sqrt{13+\sqrt{4.12}}=\sqrt{13+2\sqrt{12}}=\sqrt{\left(\sqrt{12}+1\right)^2}\)

\(=\sqrt{12}+1=2\sqrt{3}+1\)

\(\Rightarrow\sqrt{5-\sqrt{13+\sqrt{48}}}=\sqrt{5-2\sqrt{3}-1}=\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}\)

\(=\sqrt{3}-1\)

\(\Rightarrow\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}=\sqrt{3+\sqrt{3}-1}=\sqrt{2+\sqrt{3}}\)

\(\Rightarrow\sqrt{\dfrac{4+2\sqrt{3}}{2}}=\sqrt{\dfrac{\left(\sqrt{3}+1\right)^2}{2}}=\dfrac{\sqrt{3}+1}{\sqrt{2}}\)

\(\Rightarrow2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}==2.\dfrac{\sqrt{3}+1}{\sqrt{2}}=\sqrt{6}+\sqrt{2}\)

2) biến đổi khúc sau như câu 1:

\(\Rightarrow\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}=\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}\)

\(=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)

4) Ta có: \(\sqrt{30-2\sqrt{16+6\sqrt{11+4\sqrt{4-2\sqrt{3}}}}}\)

\(=\sqrt{30-2\sqrt{16+6\sqrt{11+4\left(\sqrt{3}-1\right)}}}\)

\(=\sqrt{30-2\sqrt{16+6\sqrt{7+4\sqrt{3}}}}\)

\(=\sqrt{30-2\sqrt{16+6\left(2+\sqrt{3}\right)}}\)

\(=\sqrt{30-2\sqrt{28+6\sqrt{3}}}\)

\(=\sqrt{30-2\left(3\sqrt{3}+1\right)}\)

\(=\sqrt{28-6\sqrt{3}}=3\sqrt{3}-1\)

5) Ta có: \(\dfrac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\)

\(=\dfrac{5\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}-\sqrt{2}\right)^2}{\sqrt{75}-5\sqrt{2}}\)

\(=\dfrac{5\left(\sqrt{3}-\sqrt{2}\right)}{5\left(\sqrt{3}-\sqrt{2}\right)}=1\)