<li><div class="btn-group">
<button type="button" class="btn btn-link dropdown-toggle" data-toggle="dropdown" aria-expanded="false">
<span class="glyphicon glyphicon-wrench" aria-hidden="true"></span>
</button>
<ul class="dropdown-menu" role="menu">
<li><a href="#">Action</a></li>
<li><a href="#">Another action</a></li>
<li><a href="#">Something else here</a></li>
<li class="divider"></li>
<li class="divider"></li>
<li><a href="#">Separated link</a></li>
</ul>
</div></li>
li {
display: inline;
}
<div class="btn-group">
<button type="button" class="btn btn-link dropdown-toggle" data-toggle="dropdown" aria-expanded="false">
<span class="glyphicon glyphicon-wrench" aria-hidden="true"></span>
</button>
<ul class="dropdown-menu" role="menu">
<li><a href="#">Action</a></li>
<li><a href="#">Another action</a></li>
<li><a href="#">Something else here</a></li>
<li class="divider"></li>
<li><a href="#">Separated link</a></li>
</ul>
</div>
<html>
<header>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap.min.css">
<!-- Optional theme -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap-theme.min.css">
<link rel="stylesheet" href="styles.css">
<html>
<header>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap.min.css">
<!-- Optional theme -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/css/bootstrap-theme.min.css">
<link rel="stylesheet" href="styles.css">
</header>
<body>
<div class="btn-group">
<button type="button" class="btn btn-link dropdown-toggle" data-toggle="dropdown" aria-expanded="false">
<span class="glyphicon glyphicon-wrench" aria-hidden="true"></span>
</button>
<ul class="dropdown-menu" role="menu">
<li><a href="#">Action</a></li>
<li><a href="#">Another action</a></li>
<li><a href="#">Something else here</a></li>
<li class="divider"></li>
<li><a href="#">Separated link</a></li>
</ul>
</div>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
</body>
</html>
<!-- jQuery (necessary for Bootstrap's JavaScript plugins) -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.2/jquery.min.js"></script>
<!-- Include all compiled plugins (below), or include individual files as needed -->
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
</script>
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1">
<!-- The above 3 meta tags *must* come first in the head; any other head content must come *after* these tags -->
<title>Bootstrap 101 Template</title>
<!-- Bootstrap -->
<link href="css/bootstrap.min.css" rel="stylesheet">
<!-- HTML5 shim and Respond.js for IE8 support of HTML5 elements and media queries -->
<!-- WARNING: Respond.js doesn't work if you view the page via file:// -->
<!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.2/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->
</head>
<body>
<h1>Hello, world!</h1>
<!-- jQuery (necessary for Bootstrap's JavaScript plugins) -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.2/jquery.min.js"></script>
<!-- Include all compiled plugins (below), or include individual files as needed -->
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.4/js/bootstrap.min.js"></script>
</body>
</html>
.dropdown ul.dropdown-menu:before {
content: "";
border-bottom: 10px solid #fff;
border-right: 10px solid transparent;
border-left: 10px solid transparent;
position: absolute;
top: -10px;
right: 16px;
z-index: 10;
}
The script work ok without the display:inline, so remove this otherwise you won't see the divider and may have other issue.
You have an extra <li class="divider"></li> that can be removed.