You have an algebraic expression involving two terms with a variable \( v \). The expression is:

\[
\frac{3}{2v^2} - \frac{4}{7v}
\]

To combine these terms or simplify further, it would be necessary to find a common denominator. Here’s how you can approach this:

### Step 1: Express both terms with a common denominator.
The denominators are \( 2v^2 \) and \( 7v \). To find a common denominator, take the least common multiple (LCM) of \( 2v^2 \) and \( 7v \), which is \( 14v^2 \).

### Step 2: Rewrite each fraction with the common denominator.
\[
\frac{3}{2v^2} = \frac{3 \times 7}{14v^2} = \frac{21}{14v^2}
\]
\[
\frac{4}{7v} = \frac{4 \times 2v}{14v^2} = \frac{8v}{14v^2}
\]

### Step 3: Subtract the fractions.
Now that both terms have the same denominator, you can subtract the numerators:
\[
\frac{21}{14v^2} - \frac{8v}{14v^2} = \frac{21 - 8v}{14v^2}
\]

### Final Answer:
The simplified expression is:
\[
\frac{21 - 8v}{14v^2}
\]

Would you like further details or explanations on any of these steps?

### Related Questions:
1. How do you find the least common denominator between two algebraic fractions?
2. How do you simplify expressions with variable exponents in the denominator?
3. Can this expression be simplified further if \( v \) is given a specific value?
4. How do you subtract fractions with different denominators in algebra?
5. What are the implications of having \( v = 0 \) in this expression?

**Tip:** Always check for possible factorizations or common factors before simplifying algebraic expressions.

Learn how to simplify the algebraic expression 3/2v^2 - 4/7v by finding a common denominator and subtracting fractions. This solution covers key algebraic concepts like rational expressions, LCM, and fraction subtraction, making it suitable for students in Grades 8-10.

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