"clear up the problem" is correct and usable in written English.
You would use this expression to refer to solving, resolving, or clarifying something. Example: "Let's try to clear up the problem before the end of the meeting."
Replacing its center bearing assembly should clear up the problem.
Replacing the belt will clear up the problem.
They hoped that this letter of theirs might suffice to clear up the problem for me.
T.S.B. TJ21108 issued on Oct. 5 said a damper on vehicles with single-piston calipers should clear up the problem.
If restarting the computer seems to clear up the problem temporarily, odds are the mouse glitch lies with software.
Choosing to reset the browser might clear up the problem, but it also deletes saved passwords, cookies and records of your surfing history.
If you have been having nagging, quirky problems with your Mac's performance or frequent unexplained crashes, sometimes a clean install of fresh system software can help clear up the problems.
Despite the trillions of won that it has already injected into the financial system (and the 50 trillion won that it plans to spend to complete its financial reforms by February), the government has failed to clear up the problems created by the investment trusts.
But when it received complaints from the State Police, he said, Smith & Wesson modified the ejector and cleared up the problem.
They imposed moratoriums while saying they were clearing up the problem, but by then a range of federal and state investigations were under way.
It's a makeshift solution that barely clears up the problem of the legal system not seeing the children they have raised as their children.
