https://file.aiquickdraw.com/mathbot/file/1725521605339arsv7pyv.jpg

The image you provided is slightly distorted due to interference patterns, but I can make out the mathematical problem as follows:

It appears the question is related to simplifying or solving an algebraic expression involving fractions. I will do my best to extract and solve it:

Expression from the image:

\[
\frac{a + b}{b} = \frac{a}{b} + 1
\]

There are four multiple-choice options:
1. \(\frac{a}{b}\)
2. \(\frac{b}{a}\)
3. \(1\)
4. \(\frac{1}{a}\)

Let's break it down:

We are given:
\[
\frac{a + b}{b}
\]

This expression can be split as:
\[
\frac{a + b}{b} = \frac{a}{b} + \frac{b}{b} = \frac{a}{b} + 1
\]

Therefore, the correct expression is \(\frac{a}{b} + 1\), which matches the right-hand side. So, the answer simplifies to:

\[
\frac{a}{b} + 1
\]

Thus, the answer should correspond to \(1\) (Option 3).

Would you like more details on how this is derived, or do you have any questions? Here are some additional problems related to this concept:

1. How do you simplify the expression \(\frac{x + y}{y}\)?
2. Can you solve \(\frac{c + d}{d} = \frac{c}{d} + 1\) for \(d\)?
3. What happens when the denominator is a negative number in these types of expressions?
4. How does this approach change for complex numbers instead of real numbers?
5. How do you generalize this result for \(n\) variables?

**Tip:** Always break down expressions into simpler parts, especially when dealing with fractions or algebraic terms, to identify common terms easily.

Simplify the algebraic expression: \(\frac{a + b}{b}\). Multiple-choice options: 1. \(\frac{a}{b}\), 2. \(\frac{b}{a}\), 3. \(1\), 4. \(\frac{1}{a}\).

Learn how to simplify the algebraic expression \(\frac{a + b}{b}\) with step-by-step guidance. This problem focuses on simplifying fractions, a key concept in algebra, suitable for students in Grades 6-8.

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