1. \((2x+1)^2+(x+1)^2=6x+47\)

2. \(3y^2-20=160-2y^2\)

3. \((x-7)(x-9)=195\)

4. \(3x- \cfrac{24}{x}=\cfrac{x}{3} , x≠0\)

5. \(\cfrac{x}{3}+\cfrac{3}{x}=\cfrac{15}{x} ,x≠0\)

6. \(10x-\cfrac{1}{x}=3,x≠0\)

7. \(\cfrac{2}{x^2} -\cfrac{5}{x}+2=0,x≠0\)

8. \(\cfrac{(x-2)}{(x+2)}+6\left(\cfrac{x-2}{x-6}\right)=1,x≠-2,6\)

9. \(\cfrac{1}{x-3}-\cfrac{1}{x+5}=\cfrac{1}{6} ,x≠3,-5\)

10. \(\cfrac{x}{x+1}-\cfrac{x+1}{x}=2\cfrac{1}{12} ,x≠0,-1\)

11. \(\cfrac{ax+b}{a+bx}=\cfrac{cx+d}{c+dx} , \) \([a≠b,c≠d],\) \(x≠\cfrac{a}{b},-\cfrac{c}{d}\)

12. \((2x+1)+\cfrac{3}{2x+1}=4,x≠-\cfrac{1}{2}\)

13. \(\cfrac{x+1}{2}+\cfrac{2}{x+1}=\cfrac{x+1}{3}\) \(+\cfrac{3}{x+1} \) \( -\cfrac{5}{6},x≠-1\)

14. \(\cfrac{12x+17}{3x+1}-\cfrac{2x+15}{x+7}=\cfrac{31}{5} ,\) \(x≠-\cfrac{1}{3},\) \(-7\)

15. \(\cfrac{x+3}{x-3}+6\left(\cfrac{x-3}{x+3}\right)=5,x≠3,-3\)

16. \(\cfrac{1}{a+b+x}=\cfrac{1}{a}+\cfrac{1}{b}+\cfrac{1}{x} ,\) \(x≠0,\) \(-(a+b)\)

17. \(\left(\cfrac{x+a}{x-a}\right)^2-5\left(\cfrac{x+a}{x-a}\right)+6=0,x≠a\)

18. \(\cfrac{1}{x}-\cfrac{1}{x+b}=\cfrac{1}{a}-\cfrac{1}{a+b} ,x≠0,-b\)

19. \(\cfrac{1}{(x-1)(x-2)}\) \(+\cfrac{1}{(x-2)(x-3)} \) \(+\cfrac{1}{(x-3)(x-4)}\) \(=\cfrac{1}{6} ,\) \( x≠1,2,3,4\)

20. \(x^2-(√3+2)x+2√3=0\)

21. \(\cfrac{a}{x-a}+\cfrac{b}{x-b}=\cfrac{2c}{x-c}, x\ne a,b,c\)