Here I have created a RecyclerView app in android. In this app we have added item in RecyclerView and when we click on the item in RecyclerView the item will be removed. In this recycler view I have used notifyItem Inserted() and notifyItemRemoved() function, In below example I have described how to make add and remove items to recyclerview.

Step (1)-Create xml.layout.

<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:paddingLeft="@dimen/activity_horizontal_margin"
    android:paddingRight="@dimen/activity_horizontal_margin"
    android:paddingTop="@dimen/activity_vertical_margin"
    android:paddingBottom="@dimen/activity_vertical_margin"
    tools:context=".MainActivity"
    android:orientation="vertical">

    <TextView
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_gravity="center_horizontal"
        android:autoLink="web"
        android:text="http://android-er.blogspot.com/"
        android:textStyle="bold" />

    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:orientation="vertical">
        <EditText
            android:id="@+id/name"
            android:layout_width="fill_parent"
            android:layout_height="wrap_content"/>
        <Button
            android:id="@+id/addbutton"
            android:layout_width="fill_parent"
            android:layout_height="wrap_content"
            android:text="AddName"/>
    </LinearLayout>

    <android.support.v7.widget.RecyclerView
        android:id="@+id/myrecyclerview"
        android:layout_width="match_parent"
        android:layout_height="match_parent"/>

</LinearLayout>

Step (2)-MainActivity code-

public class MainActivity extends ActionBarActivity implements RecyclerViewAdapter.OnItemClickListener{

    private RecyclerView myRecyclerView;
    private LinearLayoutManager linearLayoutManager;
    private RecyclerViewAdapter myRecyclerViewAdapter;

    EditText name;
    Button btnAdd;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        myRecyclerView = (RecyclerView)findViewById(R.id.myrecyclerview);

        linearLayoutManager =
                new LinearLayoutManager(this, LinearLayoutManager.VERTICAL, false);
        linearLayoutManager =
                new LinearLayoutManager(this, LinearLayoutManager.HORIZONTAL, false);
        myRecyclerViewAdapter = new RecyclerViewAdapter(this);
        myRecyclerViewAdapter.setOnItemClickListener(this);
        myRecyclerView.setAdapter(myRecyclerViewAdapter);
        myRecyclerView.setLayoutManager(linearLayoutManager);

        name = (EditText)findViewById(R.id.name);
        btnAdd = (Button)findViewById(R.id.addbutton);
        btnAdd.setOnClickListener(new View.OnClickListener(){
            @Override
            public void onClick(View v) {
                String newName = nameField.getText().toString();

                if(!newName.equals("")){
                    if(myRecyclerViewAdapter.getItemCount()>1){
                        myRecyclerViewAdapter.add(1, newName);
                    }else{
                        myRecyclerViewAdapter.add(0, newName);
                    }
                }
            }
        });
    }

    @Override
    public void onItemClick(RecyclerViewAdapter.ItemHolder item, int position) {
        Toast.makeText(this,
                "Remove " + position + " : " + item.getItemName(),
                Toast.LENGTH_SHORT).show();
        myRecyclerViewAdapter.remove(position);
    }
}