https://file.aiquickdraw.com/mathbot/file/1726155517156rolnw7b9.jpg

The equation you provided is:

\[
\frac{6}{v^2 - 7v + 12} = \frac{-3v}{v - 4}
\]

Let's solve this step by step.

### Step 1: Cross multiply
We will first cross-multiply to eliminate the fractions:

\[
6(v - 4) = -3v(v^2 - 7v + 12)
\]

### Step 2: Simplify both sides

Expanding both sides:

\[
6v - 24 = -3v(v^2 - 7v + 12)
\]
Expanding the right-hand side:

\[
6v - 24 = -3v^3 + 21v^2 - 36v
\]

### Step 3: Bring all terms to one side

Move all terms to one side to get a cubic equation:

\[
3v^3 - 21v^2 + 42v - 24 = 0
\]

### Step 4: Solve the cubic equation

Now, we solve this cubic equation for \(v\). I'll calculate the solutions for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through solving the cubic equation manually, or perhaps assist with a different problem?

Let me know if you'd like more details, and feel free to ask about the following topics:
1. How to expand polynomials.
2. Methods to solve cubic equations.
3. Factoring cubic expressions.
4. Understanding the discriminant for cubic equations.
5. Verifying solutions for polynomial equations.

**Tip:** When solving higher-order polynomial equations, checking for simple roots using synthetic division or trial values can help simplify the problem.

Solve for v. \frac{6}{v^2 - 7v + 12} = \frac{-3v}{v - 4}

This page provides a step-by-step solution for solving the rational equation involving cross-multiplication and solving a cubic equation. The equation \frac{6}{v^2 - 7v + 12} = \frac{-3v}{v - 4} leads to a cubic equation after simplification, ideal for high school students in grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation