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The image contains a set of mathematical problems, primarily involving fractions and algebraic expressions. I'll break them down and solve a few problems from each section.

**Problem 14: Simplify the following algebraic fractions.**

1. \(\frac{1}{x} + \frac{2}{x + 2}\)
   - The least common denominator (LCD) is \(x(x + 2)\), so the expression becomes:
     \[
     \frac{1(x + 2) + 2x}{x(x + 2)} = \frac{x + 2 + 2x}{x(x + 2)} = \frac{3x + 2}{x(x + 2)}
     \]
   - The simplified form is \(\frac{3x + 2}{x(x + 2)}\).

2. \(\frac{x^2 - 2}{x + 2x}\)
   - Simplify the denominator first: \(x + 2x = 3x\), so the expression becomes:
     \[
     \frac{x^2 - 2}{3x}
     \]
   - The simplified form is \(\frac{x^2 - 2}{3x}\).

3. \(\frac{x^2 + x - 6}{x^2 - 4}\)
   - Factor both the numerator and the denominator:
     \[
     \frac{(x - 2)(x + 3)}{(x - 2)(x + 2)}
     \]
   - Cancel the common factor \((x - 2)\), so the simplified expression is:
     \[
     \frac{x + 3}{x + 2}
     \]

4. \(\frac{x^2 + 4x + 3}{x - 3}\)
   - Factor the numerator:
     \[
     \frac{(x + 1)(x + 3)}{x - 3}
     \]
   - Since no common factors exist between the numerator and the denominator, the expression remains:
     \[
     \frac{(x + 1)(x + 3)}{x - 3}
     \]

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**Problem 15: Fraction calculations.**

1. \(\frac{150\%}{60\%}\)
   - Convert percentages to fractions: \(\frac{150}{100}\) and \(\frac{60}{100}\), so:
     \[
     \frac{150}{100} \div \frac{60}{100} = \frac{150}{100} \times \frac{100}{60} = \frac{150}{60} = 2.5
     \]
   - The result is \(2.5\).

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Would you like detailed solutions for the remaining problems or have any further questions?

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Here are 5 related questions for practice:
1. How do you find the least common denominator (LCD) for two algebraic fractions?
2. How do you simplify a complex fraction involving binomials in the numerator and denominator?
3. What is the process for factoring quadratic expressions?
4. Can all algebraic fractions be simplified by factoring? Why or why not?
5. How do you convert percentages into fractions?

**Tip:** When simplifying algebraic fractions, always check if the numerator and denominator can be factored to cancel common terms.

Simplify the following algebraic fractions and calculate the given expressions, as shown in the image.

This page provides step-by-step solutions for simplifying algebraic fractions and percentage calculations. Key topics include factoring quadratic equations, adding fractions, and converting percentages to fractions.

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