https://r2.erweima.ai/mathbot/image/172722431770444fwdr6c.jpg

The given expression is:

\[
\frac{-2x^2 + 46x - 3}{30x^3 + 39x^2 - 9x}
\]

I can simplify this expression by factoring both the numerator and the denominator. Let me work through that:

### Step 1: Factor the numerator
The numerator is \(-2x^2 + 46x - 3\). It does not appear to factor nicely into integers, so we will leave it as is for now.

### Step 2: Factor the denominator
The denominator is \(30x^3 + 39x^2 - 9x\). We can factor out a common factor of \(3x\) from the denominator:

\[
30x^3 + 39x^2 - 9x = 3x(10x^2 + 13x - 3)
\]

Now, the denominator becomes \(3x(10x^2 + 13x - 3)\).

### Step 3: Final form
Thus, the expression simplifies to:

\[
\frac{-2x^2 + 46x - 3}{3x(10x^2 + 13x - 3)}
\]

Further factoring of the quadratic terms does not seem straightforward, so this is the simplified form of the expression.

Do you have any questions or need further steps for specific cases (e.g., finding zeros, domain, or limits)?

---

Here are 5 related questions:
1. How do we find the zeros of the rational function?
2. What is the domain of this rational expression?
3. How does the expression behave as \(x\) approaches infinity?
4. Can this function be further simplified or evaluated for specific values of \(x\)?
5. How can we apply this to solve real-world problems?

**Tip:** When simplifying rational expressions, always look for common factors that can be factored out to reduce the complexity of the expression.

Simplify the algebraic expression: (-2x^2 + 46x - 3) / (30x^3 + 39x^2 - 9x)

Learn how to simplify the rational expression (-2x^2 + 46x - 3) / (30x^3 + 39x^2 - 9x) by factoring both the numerator and denominator. This step-by-step guide will help you master rational functions and algebraic simplifications. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation