JSFiddle - React, Tailwind, and code Playground

HTML

<script src="http://code.jquery.com/jquery-migrate-1.2.1.min.js"></script>
<div class="rbTrainingPlacesBlock">
    <div class="rbTrainingAddedPlace">
        <div><span>Дата окончания</span>
        </div>
        <div>
            <label for="rbtrainingplace1">Место учебы</label>
            <input type="text" name="rbtrainingplace[1]" id="rbtrainingplace1" placeholder="$rbtrainingplace[1]">
        </div>
        <div>
            <label for="rbtrainingsubject1">Название тренинга, курса</label>
            <input type="text" name="rbtrainingsubject[1]" id="rbtrainingsubject1" placeholder="$rbtrainingsubject[1]">
        </div>
    </div>
    <!-- rbEduAddedPlace -->
</div>
<!-- rbEduPlacesBlock -->
<div class="rbTrainingPlaceAddButton"><a href="javascript://" id="addTrainingPlace">Добавить тренинг, курс</a>
</div>

CSS

a#addTrainingPlace {
    padding: 10px 10px 10px 30px;
    background: lightgreen url(http://ibchrdev.pineapple-design.ru/forms2/resumebuilder20/img/iconaddblock.png) no-repeat 10px center;
    display: inline-block;
    margin: 5px 0;
    text-decoration: none;
    font: 10pt arial, helvetica, sans-serif;
    border-radius: 7px;
    color: #000;
    transition: .2s;
    box-sizing: border-box;
    -webkit-box-sizing: border-box;
    -moz-box-sizing: border-box;
}
a#addTrainingPlace:hover {
    background-color: orange;
    color: #fff;
}
.rbTrainingAddedPlace {
    width: 100%;
    display: block;
    background-color: #eee;
    margin: 10px 0;
    padding: 10px 10px 5px 10px;
    box-sizing: border-box;
    -webkit-box-sizing: border-box;
    -moz-box-sizing: border-box;
}
.rbTrainingAddedPlace span, .rbTrainingAddedPlace label {
    width: 325px;
    display: inline-block;
}
.rbTrainingAddedPlace input[type=text] {
    width: 250px;
    height: 30px;
    margin-bottom: 5px;
    border: 1px solid #ccc;
    background-color: #fff;
    border-radius: 4px;
    padding: 5px 6px;
}
.rbTrainingAddedPlace select {
    width: 122px;
    height: 30px;
    border: 1px solid #ccc;
    border-radius: 4px;
    margin: 0 6px 5px 0;
    box-sizing: border-box;
    -webkit-box-sizing: border-box;
    -moz-box-sizing: border-box;
}
.rbTrainingAddedPlace:after {
    display: block;
    content:'';
    clear: both;
}
#deleteTrainingPlace {
    width: 16px;
    height: 16px;
    display: inline-block;
    background: transparent url(http://ibchrdev.pineapple-design.ru/forms2/resumebuilder20/img/icondeleteblock.png) no-repeat;
    position: relative;
    float: right;
}
.rbTrainingPlaceAddButton {
    padding-bottom: 15px;
    margin-bottom: 15px;
    border-bottom: 1px dashed #ccc;
}

JavaScript

// Add / delete trainings
 var trainingBlock = $('.rbTrainingPlacesBlock');
 var countTraining = $('div.rbTrainingPlacesBlock div.rbTrainingAddedPlace').size() + 1;
 $('#addTrainingPlace').live('click', function () {
     $('<div class="rbTrainingAddedPlace"><a href="javascript://" id="deleteTrainingPlace"></a><div><label for="rbtrainingplace' + countTraining + '">Место учебы</label><input type="text" name="rbtrainingplace[' + countTraining + ']" id="rbtrainingplace' + countTraining + '" placeholder="$rbtrainingplace[' + countTraining + ']"></div><div><label for="rbtrainingsubject' + countTraining + '">Факультет, квалификация, специальность</label><input type="text" name="rbtrainingsubject[' + countTraining + ']" id="rbtrainingsubject' + countTraining + '" placeholder="$rbtrainingsubject[' + countTraining + ']"></div></div>').appendTo(trainingBlock);

     countTraining++;
     return false;
 });
 $('#deleteTrainingPlace').live('click', function () {
     if (countTraining > 2) {
         $(this).parents('div.rbTrainingAddedPlace').remove();
         countTraining--;
         var counter=1;
        $('input[name^="rbtrainingplace"]').each(function(){
            $(this).attr('name','rbtrainingplace['+counter+']');
            $(this).attr('placeholder','rbtrainingplace['+counter+']');
            counter++;
        });
     }
     return false;
 });