https://file.aiquickdraw.com/mathbot/file/1726750928241y0dief8j.jpg

In the image, the problem asks you to add or subtract two rational expressions:

\[
\frac{4}{y+6} + \frac{5}{y-2}
\]

It seems your submission was:

\[
\frac{9y + 22}{(y+6)(y-2)}
\]

but this was marked incorrect.

Let's work through the solution step-by-step:

### Step 1: Find a Common Denominator
The common denominator for the expressions \( \frac{4}{y+6} \) and \( \frac{5}{y-2} \) is the product of the two denominators: \((y+6)(y-2)\).

### Step 2: Rewrite Each Fraction with the Common Denominator

Rewrite each fraction with the common denominator:

\[
\frac{4}{y+6} = \frac{4(y-2)}{(y+6)(y-2)} = \frac{4y - 8}{(y+6)(y-2)}
\]

\[
\frac{5}{y-2} = \frac{5(y+6)}{(y+6)(y-2)} = \frac{5y + 30}{(y+6)(y-2)}
\]

### Step 3: Add the Numerators

Now, add the numerators:

\[
(4y - 8) + (5y + 30) = 9y + 22
\]

Thus, the resulting expression becomes:

\[
\frac{9y + 22}{(y+6)(y-2)}
\]

### Step 4: Final Check

This matches the form of the answer you submitted, so the mathematical process is correct. However, there might be some other detail that the system flagged, such as formatting or specific instructions. For example, it might expect a fully expanded or factored form in some cases. Make sure to double-check the instructions and the formatting requirements (such as spacing or parentheses).

Would you like more detailed steps, or is there anything else unclear?

### Related Questions:
1. How do you factor quadratic expressions?
2. What is the procedure for multiplying rational expressions?
3. How do you simplify complex fractions?
4. Why is finding a common denominator important when adding fractions?
5. How can you check for errors when solving rational expressions?

**Tip:** Always ensure your answer follows the exact formatting and syntax required by online systems like WeBWorK, as minor formatting issues can sometimes result in correct answers being marked incorrect.

Add or subtract the rational expressions to a single rational expression: 4/(y+6) + 5/(y-2)

This problem involves adding two rational expressions with different denominators. The solution requires finding a common denominator and simplifying the result. Learn the step-by-step approach to solving rational expressions for Grades 8-10.

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