https://r2.erweima.ai/mathbot/image/1725895844321ezjpl5aq.jpg

To simplify the given algebraic fraction:

\[
\frac{x^2 - 3x}{x^2 + 3x}
\]

**Step 1: Factor the numerator and the denominator.**

- The numerator \(x^2 - 3x\) can be factored as:
  \[
  x(x - 3)
  \]

- The denominator \(x^2 + 3x\) can be factored as:
  \[
  x(x + 3)
  \]

So, the fraction becomes:

\[
\frac{x(x - 3)}{x(x + 3)}
\]

**Step 2: Simplify the fraction by canceling the common factor \(x\).**

As long as \(x \neq 0\), the \(x\) in the numerator and denominator cancels out:

\[
\frac{x(x - 3)}{x(x + 3)} = \frac{x - 3}{x + 3}
\]

Thus, the simplified expression is:

\[
\frac{x - 3}{x + 3}
\]

### Would you like further details or have any questions?

---

Here are 5 related questions to further your understanding:

1. How would you simplify \(\frac{x^2 - 4x}{x^2 + 2x}\)?
2. What happens if \(x = 0\) in the original expression?
3. Can you find the domain of the simplified expression \(\frac{x - 3}{x + 3}\)?
4. What would be the result of simplifying \(\frac{x^2 - 9}{x^2 - 1}\)?
5. How do you simplify the fraction \(\frac{x^2 + x - 6}{x^2 + 2x + 1}\)?

**Tip:** Always check for common factors in the numerator and denominator before simplifying algebraic fractions.

Simplifica la fracción algebraica: (x^2 - 3x) / (x^2 + 3x).

Learn how to simplify the algebraic fraction (x^2 - 3x) / (x^2 + 3x) with step-by-step instructions. This problem involves factoring expressions and canceling common factors. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation