To solve the equation \( \frac{6}{x-1} = \frac{x}{x-2} \), we can cross-multiply:

\[
6(x - 2) = x(x - 1)
\]

Expanding both sides:

\[
6x - 12 = x^2 - x
\]

Rearranging all terms to one side gives:

\[
x^2 - 7x + 12 = 0
\]

Next, we can factor this quadratic equation:

\[
(x - 3)(x - 4) = 0
\]

Thus, the solutions are:

\[
x = 3 \quad \text{or} \quad x = 4
\]

Make sure to check that these values do not make the denominators zero. 

Would you like to explore further details or have any questions? Here are some related questions you might consider:

1. How can we verify the solutions?
2. What would happen if we had a different constant on the left side?
3. Can we solve this using another method, like completing the square?
4. How do the solutions affect the original equation graphically?
5. What restrictions exist for \(x\) based on the original denominators?

**Tip:** Always check your solutions in the original equation to ensure they don’t result in division by zero.

Explore the solution to the equation 6/(x-1) = x/(x-2) with detailed steps including cross-multiplication and factoring. This problem emphasizes key algebraic techniques suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation