https://file.aiquickdraw.com/mathbot/file/1726386280095nnuwbyfs.jpg

The expression in the image is:

\[
\frac{4}{v} - \frac{3}{v + 1}
\]

To simplify or combine these two fractions, let's proceed by finding a common denominator.

1. The denominator of the first fraction is \( v \).
2. The denominator of the second fraction is \( v + 1 \).

### Step-by-Step Simplification:
1. The common denominator will be the product of the two denominators: \( v(v + 1) \).
2. Rewrite both fractions with this common denominator:

\[
\frac{4}{v} = \frac{4(v + 1)}{v(v + 1)} = \frac{4v + 4}{v(v + 1)}
\]

\[
\frac{3}{v + 1} = \frac{3v}{v(v + 1)}
\]

3. Now, subtract the second fraction from the first:

\[
\frac{4v + 4}{v(v + 1)} - \frac{3v}{v(v + 1)}
\]

4. Since both fractions have the same denominator, subtract the numerators:

\[
\frac{(4v + 4) - 3v}{v(v + 1)} = \frac{4v + 4 - 3v}{v(v + 1)} = \frac{v + 4}{v(v + 1)}
\]

### Final Simplified Expression:

\[
\frac{v + 4}{v(v + 1)}
\]

This is the simplified form of the expression.

Would you like further clarification or any additional details?

Here are some related questions to deepen understanding:
1. How do you find a common denominator for two fractions?
2. How can this expression be used in solving equations?
3. What is the significance of factoring in simplifying rational expressions?
4. Can this expression be solved for specific values of \( v \)?
5. What happens if \( v = -1 \)? Why does this value need special attention?

**Tip

Learn how to simplify the rational expression 4/v - 3/(v + 1) by finding a common denominator and combining the terms. This problem covers key algebraic concepts and rational expressions suitable for students in Grades 9-11.

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