The solution set of the equation is:
OA.
OB.
O…
OD.

To solve the equation , we start by simplifying the left side. The common denominator for the left-hand fractions is , or (since ).

This gives us:

Now, set this equal to the right-hand side:

Since (i.e., cannot be 5 or -5), we can multiply both sides by to eliminate the denominators, leading to:

Solving this gives:

After plugging back into the original equation to verify, it holds true. Check for restrictions: cannot equal 5 or -5, and since 13 satisfies this, the complete solution set is .

Final Answer: OA.

The equation really shows the beauty of rational expressions and their relationships! They often have restrictions where denominators can’t equal zero, which leads to those pesky restrictions you have to remember. Understanding these relationships helps prevent small errors in more complex algebra down the line.

If you want to dive deeper into rational functions and their behaviors, you might find it fascinating to study polynomial long division or look at how asymptotes work with these kinds of functions. They’re not just practical for solving equations but can also help you visualize the behavior of graphs!