Certainly! Let's simplify the expression [tex]\(\frac{4x + 2}{x}\)[/tex] step-by-step.
1. Identify the expression:
[tex]\[
\frac{4x + 2}{x}
\][/tex]
2. Separate the numerator: The numerator consists of two terms, [tex]\(4x\)[/tex] and [tex]\(2\)[/tex]. We can split this fraction into two separate fractions:
[tex]\[
\frac{4x + 2}{x} = \frac{4x}{x} + \frac{2}{x}
\][/tex]
3. Simplify each fraction individually:
- For the fraction [tex]\(\frac{4x}{x}\)[/tex]:
[tex]\[
\frac{4x}{x} = 4 \quad \text{(since } x \text{ divided by } x \text{ is 1)}
\][/tex]
- For the fraction [tex]\(\frac{2}{x}\)[/tex]:
[tex]\[
\frac{2}{x} \quad \text{(this fraction stays as is since we cannot simplify it further)}
\][/tex]
4. Combine the simplified fractions: Now, add the simplified terms together:
[tex]\[
4 + \frac{2}{x}
\][/tex]
Thus, the simplified form of the expression [tex]\(\frac{4x + 2}{x}\)[/tex] is:
[tex]\[
4 + \frac{2}{x}
\][/tex]
So, [tex]\(\frac{4x + 2}{x} = 4 + \frac{2}{x}\)[/tex].
