The expression you provided is:

\[
5x - \frac{5}{(x-3)(x^2 - 5x + 6)}
\]

First, let's simplify this step-by-step.

### Step 1: Factor the denominator
Start by factoring the quadratic in the denominator:

\[
x^2 - 5x + 6 = (x-2)(x-3)
\]

So the expression becomes:

\[
5x - \frac{5}{(x-3)(x-2)(x-3)}
\]

### Step 2: Simplify the denominator
The denominator includes \((x-3)(x-3)\), which simplifies to \((x-3)^2\). Thus, the expression now looks like:

\[
5x - \frac{5}{(x-3)^2(x-2)}
\]

### Final simplified form:

\[
5x - \frac{5}{(x-3)^2(x-2)}
\]

This is as simplified as it gets unless further specific conditions or operations (like factoring the numerator or performing partial fractions) are required.

Would you like more details or have any questions?

Here are some related questions you could explore:
1. How do you find the roots of a quadratic equation?
2. What is the process of partial fraction decomposition?
3. How do you determine the domain of rational expressions?
4. How do vertical asymptotes relate to the factors of a denominator?
5. What happens if \( x = 3 \) in the expression above?

**Tip:** Always check for common factors when simplifying rational expressions!

Learn how to simplify the rational expression 5x - 5/(x-3)(x^2 - 5x + 6) by factoring the quadratic denominator and reducing terms step-by-step. This problem covers key algebraic concepts and factoring methods. 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