https://file.aiquickdraw.com/mathbot/file/17255067369398ildpsek.png

The equation provided in the image is:

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

### Step-by-step Solution:

1. **Eliminate the denominator** by multiplying both sides of the equation by \( (x - 3) \):

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

2. **Expand** the right side:

\[
x + 4 = 2x - 6
\]

3. **Move all terms involving \( x \) to one side** and constant terms to the other side:

\[
x - 2x = -6 - 4
\]

\[
-x = -10
\]

4. **Solve for \( x \)**:

\[
x = 10
\]

Thus, the solution is \( x = 10 \).

### Check for extraneous solutions:
Since the denominator in the original equation is \( x - 3 \), \( x = 3 \) would make the denominator zero and is not allowed. However, \( x = 10 \) does not cause this issue, so it is valid.

The solution is **\( x = 10 \)**.

Would you like further details on any step, or do you have any questions? 

Here are some related questions:
1. How would you solve a rational equation with different denominators?
2. What happens when solving leads to an extraneous solution?
3. Can you solve the equation \( \frac{2x + 1}{x + 2} = 5 \)?
4. How would you handle equations with more complex rational expressions?
5. How does the distributive property work when simplifying equations?

**Tip**: Always check for values that make the denominator zero when solving rational equations!

Solve the rational equation: (x + 4) / (x - 3) = 2.

Learn how to solve the rational equation (x + 4) / (x - 3) = 2 with a step-by-step solution. This algebra problem covers concepts like eliminating denominators and simplifying linear equations. Suitable for students in Grades 8-10.

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