Comprehensive calculus worksheet designed to test students' ability to evaluate limits algebraically through two tiers of increasing difficulty.

It looks like you've uploaded a worksheet titled "Linear Algebra – Test Worksheet", which contains two tables of algebraic problems. The instructions are to solve each problem and show all work on a separate sheet of paper.

Since I can't view images directly, I’ll need you to either:

1. Describe the problems from the image (e.g., list the expressions or equations), or
2. Type out the problems from the worksheet so I can help you solve them step by step.

However, based on the visible text in your message, here’s what I can see:

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TABLE A – POINTS EACH

These appear to be simplification or solving problems involving rational expressions, exponents, and algebraic manipulation.

Examples:
1. $ \frac{3}{4}(x^2 - 2x + 1) $
2. $ \frac{1}{2}(x + 5)^2 $
3. $ \frac{x^2 - 9}{x^2 + 6x + 9} $

And so on.

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TABLE B – POINTS EACH

These seem to involve rational expressions, factoring, and solving equations.

Examples:
19. $ \frac{x^2 - 16}{x + 4} $
20. $ \frac{x^2 - 2}{x^2 - 4} $
21. $ \frac{(x + 3)^2 - 1}{x + 3} $

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If you’d like, I can walk you through how to solve these types of problems with examples.

But to give you specific solutions, please provide the full list of problems (either typed or described). For now, here’s how to approach some common types:

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🔹 Type 1: Simplify Rational Expressions

Example: $ \frac{x^2 - 9}{x^2 + 6x + 9} $

Step-by-step:
- Factor numerator: $ x^2 - 9 = (x - 3)(x + 3) $
- Factor denominator: $ x^2 + 6x + 9 = (x + 3)^2 $
- Cancel common factor: $ \frac{(x - 3)(x + 3)}{(x + 3)^2} = \frac{x - 3}{x + 3} $, $ x \neq -3 $

✔ Final Answer: $ \frac{x - 3}{x + 3} $, $ x \neq -3 $

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🔹 Type 2: Expand or Simplify Expressions

Example: $ \frac{3}{4}(x^2 - 2x + 1) $

Step-by-step:
- Distribute $ \frac{3}{4} $ to each term:
$$
\frac{3}{4}x^2 - \frac{3}{2}x + \frac{3}{4}
$$

✔ Final Answer: $ \frac{3}{4}x^2 - \frac{3}{2}x + \frac{3}{4} $

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🔹 Type 3: Solve Rational Equations

Example: $ \frac{x}{x - 2} = \frac{4}{x - 2} $

Step-by-step:
- Multiply both sides by $ x - 2 $ (note: $ x \neq 2 $)
- $ x = 4 $
- Check: $ x = 4 $ is valid since it doesn’t make denominator zero.

✔ Final Answer: $ x = 4 $

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Please reply with the full list of problems (or describe them), and I’ll solve each one with detailed steps!