Optional where clause based on user input

Already using the ability to limit data based on user input following the example:
SELECT * FROM table WHERE fieldname = '<?php $_POST[formvariable] ?>'

But how to I add an optional clause based on whether a variable has a value or not.
For example:

SELECT * FROM table
WHERE pu.user_id = <?php $current_user->ID ?>
  AND fieldname = '<?php $_POST[formvariable] ?>'

If “formvariable” is not set, I would still like to return all the rows from table.
In other words, how to omit the “and” clause based on the value of “formvariable”?