https://r2.erweima.ai/mathbot/image/1726719288436a9hcbfrj.jpg

Let's solve the equation from the image for \( x \):

\[
\frac{a - x}{b} + \frac{b}{a} = \frac{x - 2a}{a}
\]

### Step 1: Eliminate denominators by multiplying both sides of the equation by the least common denominator (LCD), which is \( ab \).

\[
ab \left( \frac{a - x}{b} + \frac{b}{a} \right) = ab \cdot \frac{x - 2a}{a}
\]

### Step 2: Distribute \( ab \) on both sides:

\[
a(a - x) + b^2 = b(x - 2a)
\]

### Step 3: Expand both sides:

\[
a^2 - ax + b^2 = bx - 2ab
\]

### Step 4: Rearrange all terms involving \( x \) on one side:

\[
a^2 + b^2 + 2ab = bx + ax
\]

### Step 5: Factor out \( x \) on the right-hand side:

\[
a^2 + b^2 + 2ab = x(b + a)
\]

### Step 6: Solve for \( x \) by dividing both sides by \( (b + a) \):

\[
x = \frac{a^2 + b^2 + 2ab}{b + a}
\]

Thus, the solution for \( x \) is:

\[
x = \frac{a^2 + b^2 + 2ab}{b + a}
\]

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

Here are 5 related questions to expand on this:
1. How do you find the least common denominator (LCD) in equations?
2. How can factoring help simplify algebraic expressions?
3. What is the process for solving equations with fractions?
4. How can you check your solution in algebraic equations?
5. How does rearranging terms help in solving equations?

**Tip:** When dealing with fractions in equations, clearing the denominators early on simplifies the problem significantly.

This detailed solution solves the equation (a - x)/b + b/a = (x - 2a)/a for x. The solution includes key algebraic concepts such as eliminating denominators, rearranging terms, and factoring. Suitable for high school students in Grades 10-12.

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