https://r2.erweima.ai/mathbot/image/1726153045450d0kzjb9o.jpg

The equation shown in the image is:

\[
\frac{3}{x + 1} = \frac{4}{x - 3}
\]

Let's solve for \(x\):

1. Cross-multiply the equation:
\[
3(x - 3) = 4(x + 1)
\]

2. Expand both sides:
\[
3x - 9 = 4x + 4
\]

3. Get all terms involving \(x\) on one side:
\[
3x - 4x = 4 + 9
\]
\[
-x = 13
\]

4. Divide by \(-1\):
\[
x = -13
\]

Thus, the solution is \(x = -13\).

Let me know if you'd like further clarification or details.

Here are five related questions for deeper understanding:
1. How do you solve equations involving fractions?
2. What are the steps for isolating variables in linear equations?
3. How do you check if a solution to a rational equation is valid?
4. What is cross-multiplication, and why is it used in rational equations?
5. How would this method change if there were more terms in the equation?

**Tip:** Always check if the solution makes the denominator zero in the original equation—if it does, it's invalid!

Learn how to solve the rational equation 3/(x+1) = 4/(x-3) using cross-multiplication and simple algebraic steps. Suitable for students in Grades 7-9.

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