Matching Brackets

You're given the opportunity to write software for the Bracketeer™, an ancient but powerful mainframe. The software that runs on it is written in a proprietary language. Much of its syntax is familiar, but you notice lots of brackets, braces and parentheses. Despite the Bracketeer™ being powerful, it lacks flexibility. If the source code has any unbalanced brackets, braces or parentheses, the Bracketeer™ crashes and must be rebooted. To avoid such a scenario, you start writing code that can verify that brackets, braces, and parentheses are balanced before attempting to run it on the Bracketeer™.

Given a string containing brackets [], braces {}, parentheses (), or any combination thereof, verify that any and all pairs are matched and nested correctly. Any other characters should be ignored. For example, "{what is (42)}?" is balanced and "[text}" is not.