I am working on my 2023 taxes. In 2022 I built an addition on my home for the purposes of a rental suite which I started renting in 2023. What can I claim in capital x?

If you didn't report rental in 2022 then you won't be able to use the costs of 2022.
You can claim the FMV of the properties to calculate CCA in 2023 return, for example, on furniture and appliances.

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