`1.3`

`a)7/(2sqrt3-5)-7/(2sqrt3+5)`

`=(7(2sqrt3+5))/((2sqrt3+5)(2sqrt3-5))-(7(2sqrt3-5))/((2sqrt3-5)(2sqrt+5))`

`=(14sqrt3+35-14sqrt3+35)/(12-25)`

`=70/(-13)`

`=-70/13`

`b`

`1/(sqrt11+sqrt12)+1/(sqrt12+sqrt13)`

`=(sqrt12-sqrt11)/((sqrt12+sqrt11)(sqrt12-sqrt11))+(sqrt13-sqrt12)/((sqrt13-sqrt12)(sqrt12+sqrt13)`

`=sqrt12-sqrt11+sqrt13-sqrt12`

`=sqrt13-sqrt11`

`c`

`(-1)/(2-sqrt5)+4/(sqrt5-3)`

`=1/(sqrt5-2)+4/(sqrt5-3)`

`=(sqrt5-3)/((sqrt5-3)(sqrt-2))+(4(sqrt5-2))/((sqrt5-2)(sqrt5-3))`

`=(sqrt5-3+4sqrt5-2)/((sqrt5-2)(sqrt2+3))`

`=(3sqrt5-5)/((sqrt5-3)(sqrt5-2))`

`=(-sqrt5(sqrt5-3))/((sqrt5-3)(sqrt5-2)`

`=(-sqrt5)/(sqrt5-2)`

`=sqrt5/(2-sqrt5`