4D

5D

6D

7A

a: \(M=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}\)

b: \(N=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}\)

1. \(M=\dfrac{5}{x-1}-\dfrac{8}{x^2-1}-\dfrac{4}{x+1}\left(x\ne\pm1\right).\)

\(M=\dfrac{5\left(x+1\right)-8-4\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\)\(M=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}\)

\(M=\dfrac{1}{x-1}.\)

2. \(N=\dfrac{5}{x-1}+\dfrac{8}{1-x^2}-\dfrac{4}{x+1}\left(x\ne\pm1\right).\)

\(N=\dfrac{5\left(x+1\right)-8-4\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{5x+5-8-4x+4}{\left(x-1\right)\left(x+1\right)}\)

\(N=\dfrac{x+1}{\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x-1}.\)

3. \(Q=\dfrac{1}{2x-1}-\dfrac{4}{4x^2-1}-\dfrac{2}{2x+1}\left(x\ne\pm\dfrac{1}{2}\right).\)

\(Q=\dfrac{2x+1-4-2\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{2x-3-4x+2}{\left(2x-1\right)\left(2x+1\right)}\)

\(Q=\dfrac{-2x-1}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{-1}{2x-1}.\)

4. \(F=\dfrac{x+3}{x-2}+\dfrac{x+2}{3-x}+\dfrac{x+2}{x^2-5x+6}\left(x\ne2,x\ne3\right).\)

\(F=\dfrac{x+3}{x-2}-\dfrac{x+2}{x-3}+\dfrac{x+2}{\left(x-3\right)\left(x-2\right)}\)

\(F=\dfrac{\left(x+3\right)\left(x-3\right)-\left(x+2\right)\left(x-2\right)+x+2}{\left(x-2\right)\left(x-3\right)}\)

\(F=\dfrac{x^2-9-x^2+4+x+2}{\left(x-2\right)\left(x-3\right)}=\dfrac{x-3}{\left(x-2\right)\left(x-3\right)}\)

\(F=\dfrac{1}{x-2}.\)

\(b,\dfrac{1}{2}+\dfrac{13}{19}-\dfrac{4}{9}+\dfrac{6}{19}+\dfrac{5}{18}\\ =\left(\dfrac{1}{2}+\dfrac{5}{18}\right)+\left(\dfrac{13}{19}+\dfrac{6}{19}\right)-\dfrac{4}{9}\\ =\left(\dfrac{9}{18}+\dfrac{5}{18}\right)+\dfrac{19}{19}-\dfrac{4}{9}\\ =\dfrac{14}{18}+1-\dfrac{4}{9}\\ =\dfrac{7}{9}+1-\dfrac{4}{9}\\ =\left(\dfrac{7}{9}-\dfrac{4}{9}\right)+1\\ =\dfrac{3}{9}+1\\ =\dfrac{1}{3}+1\\ =\dfrac{4}{3}\)

\(c,\dfrac{-20}{23}+\dfrac{2}{3}-\dfrac{3}{23}+\dfrac{2}{5}+\dfrac{7}{15}\\ =\left(-\dfrac{20}{23}-\dfrac{3}{23}\right)+\left(\dfrac{2}{5}+\dfrac{7}{15}\right)+\dfrac{2}{3}\\ =-\dfrac{23}{23}+\left(\dfrac{6}{15}+\dfrac{7}{15}\right)+\dfrac{2}{3}\\ =-1+\dfrac{13}{15}+\dfrac{2}{3}\\ =-\dfrac{15}{15}+\dfrac{13}{15}+\dfrac{10}{15}\\ =\dfrac{8}{15}\)

\(e,\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\\ =\dfrac{5}{7}.\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\\ =\dfrac{5}{7}.\dfrac{-7}{11}\\ =-\dfrac{35}{77}\\ =-\dfrac{5}{11}\)

\(f,\dfrac{2}{11}.\dfrac{-5}{4}+\dfrac{-9}{11}.\dfrac{5}{4}+1\dfrac{3}{4}\\ =-\dfrac{2}{11}.\dfrac{5}{4}+\dfrac{-9}{11}.\dfrac{5}{4}+\dfrac{7}{4}\\=\dfrac{5}{4}.\left(-\dfrac{2}{11}+\dfrac{-9}{11}\right)+\dfrac{7}{4}\\ =\dfrac{5}{4}.1+\dfrac{7}{4}\\ =\dfrac{5}{4}+\dfrac{7}{4}\\=\dfrac{12}{4}\\ =3\)

\(h,\dfrac{7}{4}\cdot\dfrac{29}{5}-\dfrac{7}{5}\cdot\dfrac{9}{4}+3\dfrac{2}{13}\\ =\dfrac{7}{4}\cdot\dfrac{29}{5}-\dfrac{7}{4}\cdot\dfrac{9}{5}+\dfrac{41}{13}\\ =\dfrac{7}{4}\cdot\left(\dfrac{29}{5}-\dfrac{9}{5}\right)+\dfrac{41}{13}\\ =\dfrac{7}{4}\cdot\dfrac{20}{5}+\dfrac{41}{13}\\ =\dfrac{7}{4}.4+\dfrac{41}{13}\\ =\dfrac{28}{4}+\dfrac{41}{13}\\ =7+\dfrac{41}{13}\\ =\dfrac{132}{13}\)

b) Ta có: \(\sqrt{150}-\sqrt{1.6}\cdot\sqrt{60}+4.5\cdot\sqrt{2\dfrac{2}{3}}-\sqrt{6}\)

\(=5\sqrt{6}-4\sqrt{6}-\sqrt{6}+\dfrac{9}{2}\cdot\sqrt{\dfrac{8}{3}}\)

\(=\dfrac{9}{2}\cdot\dfrac{2\sqrt{2}}{\sqrt{3}}\)

\(=3\sqrt{6}\)

\(\sqrt{150}+\sqrt{1,6}.\sqrt{60}+4.5\sqrt{2\dfrac{2}{3}}-\sqrt{6}\\ =5\sqrt{6}+4\sqrt{6}+3\sqrt{6}-\sqrt{6}\\ =11\sqrt{6}\)

24 B

25 C

26 B

27 C

28 A

29 D

30 C

31 A

32 C

33 B

34 B

35 D

36 C

37 C

38 B

39 C

 1.A     2.B       3. D      4. C      5.B       6. A      7. D      8. C     9. D     10. B

11 B   12  D   13 C   14 A    15 C    16 A  17 D    18 B   19 B    20 C

21 A

22 A

1A 2B 3D 4D 5B 6A 7D 8C 9D 10B 11B 12C 13C 14A 15D 16A 17D 18B 19B 20C 21A 22A 

Cách vẽ : Đầu tiên kẻ một tia đối của tia IB ( giả sử tia IB' ), đo số đo góc AIB' . Lấy số đo chia đôi và vẽ một góc i' = số đo chia đôi đó . Vẽ tia đối của IS'  ( hình vẽ )