1 He told her she was his friend

2 Johnny told his mother he didn't know how to do that exercise

3 My brother advised me not to come back before 1 o'clock

4 Mrs Brown told her daughter to cook it in butter

5 THe pupils told the teacher to give them better marks

6 My friend asked me if I was going to leave the day after

7 My mother asked me if I had done my homework

8 I asked Bill what time he had gone to bed the night before

a, \(\frac{x+1}{2x+6}+\frac{2x+3}{x^2+3x}=\frac{x+1}{2\left(x+3\right)}+\frac{3x+2}{x\left(x+3\right)}\)

\(=\frac{x^2+x}{2x\left(x+3\right)}+\frac{6x+4}{2x\left(x+3\right)}=\frac{x^2+7x+4}{2x\left(x+3\right)}\)

b, Sua de :  \(\frac{3}{2x+6}-\frac{x-6}{2x^2+6x}=\frac{3}{2\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}\)

\(=\frac{3x}{2x\left(x+3\right)}-\frac{x-6}{2x\left(x+3\right)}=\frac{2x+6}{2x\left(x+3\right)}=\frac{1}{x}\)

Literature is my favorite subject.

I like literature the most

C

Ai làm nhanh nhất được tick!

\(A=cos^4a+cos^2a\cdot\sin^2a+\sin^2a\)

\(=cos^2a\left(cos^2a+\sin^2a\right)+\sin^2a\)

\(=cos^2a+\sin^2a=1\)

\(\dfrac{5}{2\cdot4}+\dfrac{5}{4\cdot6}+...+\dfrac{5}{48\cdot50}\\ =\dfrac{5}{2}\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{48\cdot50}\right)\\ =\dfrac{5}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)\\ =\dfrac{5}{2}\left(\dfrac{1}{2}-\dfrac{1}{50}\right)=\dfrac{5}{2}\cdot\dfrac{12}{25}=\dfrac{6}{5}\)

Ta có: \(\dfrac{5}{2\cdot4}+\dfrac{5}{4\cdot6}+...+\dfrac{5}{48\cdot50}\)

\(=\dfrac{5}{2}\cdot\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{48\cdot50}\right)\)

\(=\dfrac{5}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{48}-\dfrac{1}{50}\right)\)

\(=\dfrac{5}{2}\left(\dfrac{1}{2}-\dfrac{1}{50}\right)\)

\(=\dfrac{5}{2}\cdot\dfrac{12}{25}\)

\(=\dfrac{60}{50}=\dfrac{6}{5}\)

\(6\times\dfrac{3}{5}=\dfrac{18}{5};\dfrac{7}{2}+\dfrac{3}{10}=\dfrac{35}{10}+\dfrac{3}{10}=\dfrac{38}{10}=\dfrac{19}{5}\\ Ta.có:\dfrac{1}{10}< \dfrac{1}{2}< \dfrac{3}{5}< \dfrac{7}{10}< \dfrac{9}{10}< \dfrac{9}{7}< \dfrac{9}{5}< 3< \dfrac{18}{5}< \dfrac{19}{5}\\ \Leftrightarrow\dfrac{1}{10}< \dfrac{1}{2}< \dfrac{3}{5}< \dfrac{7}{10}< \dfrac{9}{10}< \dfrac{9}{7}< \dfrac{9}{5}< 3< 6\times\dfrac{3}{5}< \dfrac{7}{2}+\dfrac{3}{10}\)