Simplify the following expression.
5/x+b -5/x /b

Let's simplify the given expression step by step.

The expression is:

\[
\frac{5}{x} + b - \frac{\frac{5}{x}}{b}
\]

### Step 1: Simplify the Expression

Start by breaking down the expression:

\[
\frac{5}{x} + b - \frac{\frac{5}{x}}{b}
\]

The term \(\frac{\frac{5}{x}}{b}\) can be simplified further:

\[
\frac{\frac{5}{x}}{b} = \frac{5}{bx}
\]

So the expression now becomes:

\[
\frac{5}{x} + b - \frac{5}{bx}
\]

### Step 2: Find a Common Denominator

To simplify further, combine the fractions by finding a common denominator. The common denominator between \(\frac{5}{x}\) and \(\frac{5}{bx}\) is \(bx\):

\[
\frac{5 \cdot b}{bx} + \frac{bx \cdot b}{bx} - \frac{5}{bx}
\]

This simplifies to:

\[
\frac{5b}{bx} + b - \frac{5}{bx}
\]

### Step 3: Combine the Fractions

Now, combine the fractions:

\[
\frac{5b - 5}{bx} + b
\]

Factor out the common factor from the numerator in the fraction:

\[
\frac{5(b - 1)}{bx} + b
\]

### Final Simplified Expression

So, the simplified form of the expression is:

\[
\frac{5(b - 1)}{bx} + b
\]

This is the final simplified expression.

Would you like any further explanation on these steps or how to approach similar problems?

### Related Questions:
1. What happens if \(b = 1\) in the simplified expression?
2. How would the expression change if we had \( \frac{5}{x} - b + \frac{5}{bx} \)?
3. Can this expression be further simplified if \(b\) and \(x\) are specific values?
4. How does the simplification process change if there are additional terms in the numerator or denominator?
5. What are the implications of having \(b = 0\) in this expression?

### Tip:
When simplifying expressions involving fractions, always look for a common denominator to combine terms effectively. This approach often simplifies the process and reduces the complexity of the expression.

Learn how to simplify the expression 5/x + b - 5/(bx) step-by-step with a detailed solution. This problem involves algebraic concepts such as fraction simplification. Suitable for high school students and those preparing for algebra exams.

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