Short Answer 
The homeowner qualifies for the capital gains tax exemption by living in her home for at least 2 years within the last 5 years, calculating her capital gain as $150,000 from the sale, and confirming that this amount is below the $250,000 exemption limit, making her fully exempt from capital gains tax.
1. Duration of Residence
To qualify for the capital gains tax exemption, the homeowner must have lived in their home for a specific period. This requirement states that you need to have stayed in the house for at least 2 years out of the last 5 years before the sale. In this case, the woman lived in her home for 3 years, making her eligible for the exemption.
2. Calculate Capital Gain
The next step is to determine the capital gain from selling the home. This is done by subtracting the cost price of the home from the selling price. For this woman, the calculation is as follows:
- Selling price: $450,000
- Cost price: $300,000
- Capital gain: $450,000 – $300,000 = $150,000
3. Determine Tax Exemption Eligibility
Now, compare the calculated capital gain to the exemption limit. As a single homeowner, she can exclude up to $250,000 of capital gains. Since her capital gain is $150,000, which is less than the exemption limit, she is fully exempt from paying any capital gains tax upon selling her house.