https://r2.erweima.ai/mathbot/image/1726093803615z3ay7q37.jpg

The equation provided in the image is:

\[
\frac{4}{x - 3} = \frac{5}{x - 2}
\]

To solve this equation for \(x\), we can use cross-multiplication. Cross-multiply both sides:

\[
4(x - 2) = 5(x - 3)
\]

Now expand both sides:

\[
4x - 8 = 5x - 15
\]

Next, move all terms involving \(x\) to one side and constants to the other:

\[
4x - 5x = -15 + 8
\]

Simplify:

\[
-x = -7
\]

Divide by \(-1\):

\[
x = 7
\]

So, the solution is \(x = 7\).

Would you like more details or have any questions? Here are some related questions you might find useful:

1. How can you check if \(x = 7\) is a valid solution for the original equation?
2. What are the potential restrictions on the values of \(x\) in the original equation?
3. Can you solve similar rational equations involving variables in the denominator?
4. What would happen if both sides of the equation had more complex expressions, such as quadratic terms?
5. How would you graph the equation to verify the solution visually?

**Tip:** Always check for any restrictions in the denominator of rational equations to ensure the solution does not lead to division by zero.

Solve the equation 4/(x - 3) = 5/(x - 2).

Learn how to solve the rational equation 4/(x - 3) = 5/(x - 2) using cross multiplication. This step-by-step guide covers key algebraic concepts and rational equations. Suitable for students in Grades 7-9.

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