# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/20

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Question 20

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## Exercise 20

### Question

export const metadata = {
  title: "Question 20",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

The result of:

<MathContainer>
  <BlockMath math="\frac{3x}{x^2 - 4} - \frac{2}{x - 2}" />
</MathContainer>

is...


### Choices

- [ ] $$\frac{2x + 12}{x^2 - 4}$$
- [ ] $$\frac{x - 12}{x^2 - 4}$$
- [ ] $$\frac{-x + 12}{x^2 - 4}$$
- [ ] $$\frac{-2x}{x^2 - 4}$$
- [x] $$\frac{x - 4}{x^2 - 4}$$

### Answer & Explanation

export const metadata = {
  title: "Answer to Question 20",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

We are asked to simplify the following algebraic fraction:

<MathContainer>
  <BlockMath math="\frac{3x}{x^2 - 4} - \frac{2}{x - 2}" />
</MathContainer>

Notice the denominator of the first fraction, <InlineMath math="x^2 - 4" />. This can be factored into <InlineMath math="(x - 2)(x + 2)" />.

Thus, we make the denominators of both fractions the same, which is <InlineMath math="x^2 - 4" /> or <InlineMath math="(x - 2)(x + 2)" />:

<MathContainer>
  <BlockMath math="= \frac{3x}{x^2 - 4} - \frac{2(x + 2)}{(x - 2)(x + 2)}" />
  <BlockMath math="= \frac{3x}{x^2 - 4} - \frac{2(x + 2)}{x^2 - 4}" />
</MathContainer>

Now we can combine the numerators:

<MathContainer>
  <BlockMath math="= \frac{3x - 2(x + 2)}{x^2 - 4}" />
  <BlockMath math="= \frac{3x - 2x - 4}{x^2 - 4}" />
  <BlockMath math="= \frac{x - 4}{x^2 - 4}" />
</MathContainer>

So, the simplified result is <InlineMath math="\frac{x - 4}{x^2 - 4}" />.


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