32
分析:
![](http://thumb.1010pic.com/pic5/latex/151639.png)
+
![](http://thumb.1010pic.com/pic5/latex/43196.png)
=
![](http://thumb.1010pic.com/pic5/latex/6.png)
,可知
![](http://thumb.1010pic.com/pic5/latex/151639.png)
![](http://thumb.1010pic.com/pic5/latex/534512.png)
,
![](http://thumb.1010pic.com/pic5/latex/43196.png)
<
![](http://thumb.1010pic.com/pic5/latex/6.png)
,即A>12,B>12,又因A>B,可知B是一个大于13且小于32的自然数,然后分情况讨论,可分别求出A、B的值,据此解答.
解答:根据以上分析可,13<B<32,
当B=13,A=51时,
![](http://thumb.1010pic.com/pic5/latex/547300.png)
,
当B=14.A=50时,
![](http://thumb.1010pic.com/pic5/latex/547301.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=15.A=49时,
![](http://thumb.1010pic.com/pic5/latex/547302.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=16.A=48时,
![](http://thumb.1010pic.com/pic5/latex/547303.png)
=
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=17.A=47时,
![](http://thumb.1010pic.com/pic5/latex/547304.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=18.A=46时,
![](http://thumb.1010pic.com/pic5/latex/547305.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=19.A=45时,
![](http://thumb.1010pic.com/pic5/latex/547306.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=20.A=44时,
![](http://thumb.1010pic.com/pic5/latex/547307.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=21.A=43时,
![](http://thumb.1010pic.com/pic5/latex/547308.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=22.A=42时,
![](http://thumb.1010pic.com/pic5/latex/547309.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=23.A=41时,
![](http://thumb.1010pic.com/pic5/latex/547310.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=24.A=40时,
![](http://thumb.1010pic.com/pic5/latex/547311.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=25.A=39时,
![](http://thumb.1010pic.com/pic5/latex/547312.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=26.A=38时,
![](http://thumb.1010pic.com/pic5/latex/547313.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=27.A=37时,
![](http://thumb.1010pic.com/pic5/latex/547314.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=28.A=36时,
![](http://thumb.1010pic.com/pic5/latex/547315.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=29.A=35时,
![](http://thumb.1010pic.com/pic5/latex/547316.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=30.A=34时,
![](http://thumb.1010pic.com/pic5/latex/547317.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
当B=31.A=33时,
![](http://thumb.1010pic.com/pic5/latex/547318.png)
≠
![](http://thumb.1010pic.com/pic5/latex/6.png)
,
只有当B=16,A=48时,才满足A、B都是自然数,A>B,A+B=64,
![](http://thumb.1010pic.com/pic5/latex/151639.png)
+
![](http://thumb.1010pic.com/pic5/latex/43196.png)
=
![](http://thumb.1010pic.com/pic5/latex/6.png)
.
48-16=32.
故答案为:32.
点评:本题的关键是根据分数加法和的变化规律,分情况讨论B的情况,再进行解答.