To solve \( \frac{3}{4} + x - \frac{3}{2x} \), we first aim to find a common denominator for the fractional terms.

### Step 1: Identify the common denominator
The denominators are \(4\), \(1\) (for \(x\)), and \(2x\). The least common multiple (LCM) of \(4\) and \(2x\) is \(4x\). 

### Step 2: Express each term with a common denominator
We rewrite each term:

1. \( \frac{3}{4} \) becomes \( \frac{3x}{4x} \).
2. \( x \) becomes \( \frac{4x^2}{4x} \).
3. \( \frac{3}{2x} \) becomes \( \frac{6}{4x} \).

### Step 3: Combine the fractions
\[
\frac{3}{4} + x - \frac{3}{2x} = \frac{3x}{4x} + \frac{4x^2}{4x} - \frac{6}{4x}.
\]

Now, combine the numerators over the common denominator:
\[
\frac{3x + 4x^2 - 6}{4x}.
\]

### Step 4: Simplify the numerator if possible
The numerator \(3x + 4x^2 - 6\) does not factor nicely with the denominator, so the simplified form remains:

\[
\boxed{\frac{4x^2 + 3x - 6}{4x}}.
\]

Would you like more details or have any questions?

### Related Questions
1. How do you find the LCM of multiple denominators?
2. What are the steps to simplify a rational expression?
3. Can a polynomial numerator be factorable over rational numbers?
4. How do you handle variables in denominators when simplifying expressions?
5. What’s the importance of keeping a common denominator when combining terms?

**Tip:** Always check if the numerator and denominator can be simplified further by factoring or canceling common factors.

Explore how to simplify the algebraic expression 3/4 + x - 3/2x. This step-by-step guide covers key concepts like finding the least common denominator, combining fractions, and simplifying the result. Perfect for students in Grades 8-10.

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