https://file.aiquickdraw.com/mathbot/file/172613789041251uxudyl.jpg

The equation in the image is:

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

Would you like a step-by-step solution for this equation or any further details?

Here are 5 related questions to extend this:

1. How can this equation be solved for \( x \)?
2. What happens if \( a = b \) in this equation?
3. How can this equation be simplified using algebraic identities?
4. What are the constraints on \( x \) so the equation is well-defined?
5. How can this be applied in a real-world context?

**Tip**: Always check the denominators for restrictions, as they can provide critical insights about the values for which the equation is valid.

The equation in the image: \[ \frac{a}{x - a} + \frac{b}{x - b} = \frac{a + b}{x - a - b} \]

Explore how to solve the rational equation \( \frac{a}{x - a} + \frac{b}{x - b} = \frac{a + b}{x - a - b} \). This problem covers advanced algebraic concepts, such as the sum of fractions with different denominators and restrictions on variables. Suitable for Grades 10-12.

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