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Home » Pauls Online Math Notes: The Ultimate Study Guide No Student Should Miss! - Carbonext

Pauls Online Math Notes: The Ultimate Study Guide No Student Should Miss! - Carbonext

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📝 Recent Posts

A geometric sequence starts with 2 and has a common ratio of 3. What i...
The formula for the \( n \)-th term of a geometric sequence is \( a_n...
\[ a_6 = 2 \cdot 3^{6-1} = 2 \cdot 3^5 = 2 \cdot 243 = 486 \]
Simplify \( (x^2 - 9)/(x + 3) \) and state any restrictions.
Factor the numerator using the difference of squares:
\[ x^2 - 9 = (x - 3)(x + 3) \]
The expression simplifies to:
\[ rac{(x - 3)(x + 3)}{x + 3} = x - 3 \]
Restriction: \( x
eq -3 \) (to avoid division by zero).

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