Simplify the expression: \frac{3-2x}{2x-3}



To simplify the expression:

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

Notice that the numerator \( 3 - 2x \) and the denominator \( 2x - 3 \) are almost identical, except for their signs.

We can factor out a \(-1\) from either the numerator or the denominator to make them match. Let's factor \(-1\) from the denominator:

\[
2x - 3 = -(3 - 2x)
\]

Now the expression becomes:

\[
\frac{3 - 2x}{-(3 - 2x)} = -1
\]

So, the simplified expression is:

\[
-1
\]

Would you like more details on any of the steps? Here are some related questions to deepen your understanding:

1. How do you factor out a negative sign from expressions?
2. What are other common methods for simplifying algebraic expressions?
3. How can you identify when to factor in an expression?
4. Can you provide examples where this technique is used in complex equations?
5. What happens if the numerator and denominator don’t differ only by a sign?

**Tip:** Always check for patterns or common factors in both the numerator and denominator when simplifying expressions.

Simplify the expression: \frac{3-2x}{2x-3}

Learn how to simplify the rational expression \frac{3 - 2x}{2x - 3} by factoring out common terms and using the inverse property. This solution covers key algebraic concepts and is suitable for students in Grades 8-10.

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