# [Wolfram Language](https://www.wolfram.com/language/), <s>101</s> 100 bytes

```Mathematica
StringJoin[Characters@#/.(r={"L"->-"R","U"->-"D"})//.{a___,x__,b___}/;Tr@{x}==0->{a,b}/.Reverse/@r]&
```
[Try it online!](https://tio.run/##PY1BC8IwDIXv/owKotCt3mWjYE@Sg0R7EhmddG6HTahFBqW/faZzGEj48vJ46Y1vbW989zBTU0wX77rheXp1w@3YGmce3rq3XIt864rAgGVlxpBxpmdSLO6EyIOpqoqP1DVBFIerk2GMRbHPymB4HUWO9kNBVkh330xn@uGFbIQMK6YBNWrGiVCB@iFQISIsrP@LJhN5QM2bAo2Yhpr9gKBIWMI0aXQjb4pVyZIEUuiSXsbpCw "Wolfram Language (Mathematica) – Try It Online")

With some fancier formatting and comments:
```Mathematica
StringJoin[                                       (*reconvert to input format*)
  Characters@#                                    (*split into characters*)
  /. (r = {"L" -> -"R", "U" -> -"D"})             (*map L to -R and U to -D*)
  //. {a___, x__, b___} /; Tr@{x} == 0 -> {a, b}  (*delete runs that sum to 0*)
  /. Reverse /@ r                                 (*convert -R and -D back to L and U*)
]&
```
This takes a similar method to some of the others, deleting runs that sum to zero, but this one does it by replacing L and U with negative R and negative D respectively.

Another **100 byte** solution that uses a similar but distinct technique, using [SequenceReplace](http://reference.wolfram.com/language/ref/SequenceReplace.html):
```Mathematica
StringJoin@SequenceReplace[Characters@#/.(r={"L"->-"R","U"->-"D"}),{__}?(Tr@#==0&)->{}]/.Reverse/@r&
```
[Try it online!](https://tio.run/##PY3BCsIwDIbvPkYHMmFbfYHNgj1JDhrtSWSUkenATa3Vy9izz3SKOYT///Mlaa2/UGt9U9mxzse9d0133tyaTu3p8aKuIqT71VZ0XF@ss5Un91SRzGKX9wJEWqQCRSLMpLQYFklflsMqPjgV5flyvkiLfjjJDOnNmySVm49b/uGlqqXqZ8IAGjQiYYUa9FcCFyLCT5u/MQwxA3pyGgxiaHriAUFz8DtmOOMZs@GsDkgIOOFJeDlIuXs15McP "Wolfram Language (Mathematica) – Try It Online")