1/a- 1/b = 1/a+b

Multiply a+b, (1+b/a)-(a/b+1) =1.

Simplify to get b/a-a/b= 1.

2.

Suppose S△HOD=S 1.

Because AH=DH, S△AOH=S△HOD=S 1.

Then S△EOA=S□AEOH-S△AOH=3-S 1.

Because AE=BE, S△BOE=S△EOA=3-S 1.

Then s delta fob = s □ bfoe-s delta BOE = 4-(3-s1) =1+s1.

Since BF=CF, S△COF=S△FOB= 1+S 1.

Then s △ goc = s □ cgof-s △ cof = 5-(1+s1) = 4-s1.

Because CG=DG, S△DOG=S△GOC=4-S 1.

So s □ dhog = s △ hod+s △ dog = s1+(4-s1) = 4.

3.

X=3, y=4 and z=6, so that each point can be surrounded by a triangle with an included angle of 60 degrees, a hexagon with an included angle of 120 degrees and two squares with an included angle of 90 degrees.

1/x+ 1/y+ 1/z = 3/4

4.

By ab+bc+ca=abc

Divide both sides by abc to get1/a+1/b+1/c =1.

When a= 1, 1/b+ 1/c = 1, so 1/b+ 1/c=0 does not meet the requirements.

When a=2,1/2+1/b+1/c =1,so1/b+1/2.

B > a, so b=3, then1/3+1/c =1/2, so c=6.

When a=3,1/3+1/b+1/c =1,so 1/b+ 1/c=2/3.

If b=c, there is b = c = 3；; If b is not equal to c, one of b and c must be less than 3, so a=3, a >；; 3, the conditions can not be met.

So the only solution is: a=2, b=3, c=6.