https://file.aiquickdraw.com/mathbot/file/1727317092256ft89cv61.jpg

To solve the expression given in the image:

\[ \frac{16-p}{(p+4)(p-6)} + \frac{2}{p+4} \]

We first look for a common denominator, which in this case is \((p+4)(p-6)\). We need to rewrite each fraction with this common denominator:

1. The first fraction is already expressed with the denominator \((p+4)(p-6)\).
2. For the second fraction, multiply the numerator and the denominator by \(p-6\):

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

Now, add the two fractions:

\[ \frac{16-p}{(p+4)(p-6)} + \frac{2(p-6)}{(p+4)(p-6)} = \frac{16-p + 2(p-6)}{(p+4)(p-6)} \]

Simplify the numerator:

\[ 16-p + 2p - 12 = p + 4 \]

Therefore, the expression simplifies to:

\[ \frac{p+4}{(p+4)(p-6)} \]

Assuming \(p \neq -4\), we can cancel \(p+4\) from the numerator and denominator:

\[ \frac{1}{p-6} \]

Thus, the sum of the expressions in simplest terms is:

\[ \frac{1}{p-6} \]

If you have any questions or need further explanations on how I derived this, feel free to ask! Here are some related questions you might consider:

1. What would the result be if \( p = -6 \)?
2. How would you evaluate this expression for specific values of \( p \)?
3. What happens to the expression as \( p \) approaches -4?
4. Could you graph this expression to understand its behavior better?
5. What are the restrictions on the value of \( p \) in this expression?

**Tip**: When adding fractions with algebraic expressions, always look for a common denominator first to simplify the process.

Add. State the sum in simplest terms: \( \frac{16-p}{(p+4)(p-6)} + \frac{2}{p+4} \), \( p \neq -4, 6 \).

Learn how to add and simplify rational expressions with different denominators. The problem involves algebraic concepts like adding fractions with algebraic expressions and simplifying by factoring. Suitable for students in Grades 9-10.

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