Consider the use of `children` for wrapping everything in one component. Its very common to use this `children` prop.

App.js

import React, { Component } from 'react';
import { Route, Switch } from 'react-router-dom'

// import pages 
import Container from './Container';
import Greetings from './Greetings';
import Customers from './Customers';


class App extends Component {
    render() {
        return (
            <Switch>
                <Container>
                    <Route exact path="/" component={ Greetings }></Route>
                    <Route path="/customers" component={ Customers }></Route>
                </Container>
            </Switch>
        );
    }
}

export default App;

Container.js

import React, { Component } from 'react';

export default function Container({ props }) {
  return (
    <div className="wrapper-class">
      { props.children }
    </div>
  );
}