A=12/15 + 28/315

            A=8/9 

\(a,8+2\sqrt{15}=\left(\sqrt{3}+\sqrt{5}\right)^2\\ b,12+2\sqrt{35}=\left(\sqrt{7}+\sqrt{5}\right)^2\\ c,8+\sqrt{60}=8+2\sqrt{15}=\left(\sqrt{3}+\sqrt{5}\right)^2\)

a: Ta có: \(\sqrt{4+\sqrt{15}}\)

\(=\dfrac{\sqrt{8+2\sqrt{15}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{10}+\sqrt{6}}{2}\)

b: Ta có: \(\left(3-\sqrt{2}\right)\cdot\sqrt{11+6\sqrt{2}}\)

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

=9-2

=7

c: Ta có: \(\left(\sqrt{7}+\sqrt{5}\right)\cdot\sqrt{12-2\sqrt{35}}\)

\(=\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)\)

=2

a: \(\dfrac{-35}{-7}=\dfrac{35}{7}=5\)

b: \(\dfrac{42}{-21}=-\dfrac{42}{21}=-2\)

c: \(\dfrac{55}{-5}=-\dfrac{55}{5}=-11\)

d: \(\dfrac{46}{-23}=-\dfrac{46}{23}=-2\)

e: \(-30:\left(-2\right)=\dfrac{30}{2}=15\)

f: \(23\cdot\left(-4\right)=-23\cdot4=-92\)

g: \(15\cdot\left(-3\right)\cdot0=15\cdot0=0\)

h: \(-32\cdot14=-32\cdot10-32\cdot4=-320-128=-448\)

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}=2\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}\right)=2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}\right)\)

\(=2\left[\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}\right)\right]\)

\(=2.\left[\frac{1}{2}.\left(1-\frac{1}{9}\right)\right]=2.\left(\frac{1}{2}.\frac{8}{9}\right)=2.\frac{4}{9}=\frac{8}{9}\)

mả cha mày

2/3 + 2/15 + 2/35 + 2/63

= 2/1×3 + 2/3×5 + 2/5×7 + 2/7×9

= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9

= 1 - 1/9

= 8/9

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}\)

= \(\frac{4}{5}+\frac{4}{45}\)

= \(\frac{8}{9}\)

2/3 + 2/15 + 2/35 + 2/63 + 2/99

= 2/1×3 + 2/3×5 + 2/5×7 + 2/7×9 + 2/9×11

= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11

= 1 - 1/11

= 10/11

2/3+2/15+2/35+2/63+2/99

=4/5+2/15+2/63+2/99

=14/15+2/63+2/99

=304/315+2/99

=1138/1155

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{143}\)

\(=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{11\times13}\)

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

\(=1-\frac{1}{13}=\frac{12}{13}\)

Đặt \(A=\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{143}\)

\(\Rightarrow A=\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{11.13}\)

\(\Rightarrow A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\)

\(\Rightarrow A=1-\frac{1}{13}=\frac{13}{13}-\frac{1}{13}=\frac{2}{13}\)

\(=\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)

\(=2.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\right)\)

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

\(=2.\left(\frac{1}{1}-\frac{1}{11}\right)\)

\(=\frac{20}{11}\)

\(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}\)

= \(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}\)

= \(\frac{3-1}{1\times3}+\frac{5-3}{3\times5}+\frac{7-5}{5\times7}+\frac{9-7}{7\times9}+\frac{11-9}{9\times11}\)

= \(\frac{3}{1\times3}-\frac{1}{1\times3}+\frac{5}{3\times5}-\frac{3}{3\times5}+...+\frac{11}{9\times11}-\frac{9}{9\times11}\)

= \(1-\frac{1}{11}\)=\(\frac{10}{11}\)