Only you can have the home sale exclusion of capital gains of $250,000 as you have lived in the home for more than 2 years in the last 5 years.
Your ex-wife is not eligible for this exclusion.
The IRS says:
If you have lived in the house you plan to sell for more than 2 years in the last 5 years before you sell it, you are eligible for the capital gain exclusion of $250,000 ($500,000 if you file jointly).
If the capital gain is below this threshold, you do not have to report the sale on your tax return, except if you receive a form 1099-S in which case you have to report the sale but the capital gain will be excluded from taxation.
Please read this IRS document for more information.
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