Cho\(\frac{a}{b}=\frac{c}{d}\)≠1,-1,c≠0,Cm rằng

a,(\(\frac{a-b}{c-d}\))² =\(\frac{ab}{cd}\)

b,(\(\frac{a+b}{c+d}\))³ =\(\frac{a^3-b^3}{c^3-d^3}\)

Độ dài ba cạnh của 1 tam giác tỉ lệ với 2,3,4,ba chiều cao tương ứng vs 3 cạnh tỉ lệ với 3 số nào

Tìm x,y,z,t biết

a,x:y:z:t=15:7:3:1 và x-y+z-t=10

b,\(\frac{x}{5}=\frac{y}{6},\frac{y}{8}=\frac{z}{7}vàx+y-z=69\)

c,2x=3y,5y=7z và 3x+5z-7y

d,\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}và5z-3x-4y=50\)

Cho 3 số a,b,c thỏa mãn a.b.c=1

CMR:\(\frac{1}{ab+a+1}+\frac{1}{bc+b+1}+\frac{1}{abc+bc+b}=1\)

Tìm a∈Z để

a,\(\frac{2a+5}{5}-\frac{a}{5}làsốnguyên\)

b,\(\frac{2a+9}{a+3}-\frac{5a+17}{a+3}-\frac{3a}{a+3}làsốnguyên\)

Tìm x,y ϵ Z

a,\(\frac{1}{x}=\frac{1}{6}+\frac{y}{3}\)

b,\(\frac{x}{6}-\frac{1}{y}=\frac{1}{2}\)

c,\(\frac{x}{4}-\frac{1}{y}=\frac{3}{4}\)

d,\(\frac{x}{8}-\frac{2}{y}=\frac{3}{4}\)

e,\(\frac{x}{4}-\frac{2}{y}=\frac{3}{2}\)

g,\(\frac{1}{x}-\frac{1}{y}=\frac{1}{x}.\frac{1}{y}\)

x≠y≠0

Tìm x,biết

a, \(\frac{3}{\left(x+2\right)\left(x+5\right)}+\frac{5}{\left(x+5\right)\left(x+10\right)}+\frac{7}{\left(x+10\right)\left(x+17\right)}=\frac{x}{\left(x+2\right)\left(x+17\right)}\)

Với x ∉ -2,-5,-10,-17

b,\(\frac{2}{\left(x-1\right)\left(x-3\right)}+\frac{5}{\left(x-3\right)\left(x-8\right)}+\frac{12}{\left(x-8\right)\left(x-20\right)}-\frac{1}{x-20}=\frac{-3}{4}\)

Với x∉1,3,8,20

c,\(\frac{x-1}{2009}+\frac{x-2}{2008}=\frac{x-3}{2007}+\frac{x-4}{2006}\)

Điền ''if '' hoặc ''unless '' vào chỗ trống

1. ....................you had rung , he would have come

2. ...................you rang,he wouldn't come

3. I should never have found the house.................the policeman hadn't helped me

4. He wouldn't learn mich .......................he works harder

5. I won't go to the door.................I hear the bell

6. .....................my watch hadn't been right , we shouldn't have been late

7. ........................the clock had been right ,we shouldn't have been late

8. I won't write to him..............he writes to me

9. .......................you don't ring the bell,the servant won't come

10. He'll come...........................you ring the bell

Điền ''if'' hoặc ''unless'' vào chỗ trống

1. He won't speak French.......he goes to France

2.I'll go to the door............. I hear the bell

3.He wouldn't have waited...........you'd been late

4. .................you ring the bell,the servant won't come

5.He will come.............you ring the bell

6. ..................he wrote to me ,I would write to him

7. He would have come ...........you had rung

8.He would come ...............you rang

9. ................he started immediately,he would arrive by midday

10. ...........................you send a telegram now,he will get it this evening