To simplify the expression \(\frac{2}{x} - \frac{3}{x + 1} \div \frac{4}{x + 1} + \frac{5}{x}\), follow these steps:

### Step 1: Simplify the division
The expression has a division: \(\frac{3}{x + 1} \div \frac{4}{x + 1}\). To simplify this:

\[
\frac{3}{x + 1} \div \frac{4}{x + 1} = \frac{3}{x + 1} \times \frac{x + 1}{4} = \frac{3}{4}
\]

### Step 2: Substitute back into the expression
Now, substitute \(\frac{3}{4}\) back into the original expression:

\[
\frac{2}{x} - \frac{3}{4} + \frac{5}{x}
\]

### Step 3: Combine like terms
Combine the terms that have the common denominator \(x\):

\[
\frac{2}{x} + \frac{5}{x} = \frac{2 + 5}{x} = \frac{7}{x}
\]

So, the simplified expression is:

\[
\frac{7}{x} - \frac{3}{4}
\]

### Final Answer:
The simplified form of the given expression is:

\[
\frac{7}{x} - \frac{3}{4}
\]

Would you like more details on any of these steps?

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Here are 5 related questions:

1. How do you add or subtract fractions with different denominators?
2. How do you simplify a complex fraction?
3. What is the difference between multiplying and dividing fractions?
4. How do you solve equations involving fractions?
5. How can you simplify expressions with multiple fractions?

**Tip:** When dividing fractions, remember to multiply by the reciprocal of the divisor.

Learn how to simplify the expression 2/x - 3/(x + 1) / 4/(x + 1) + 5/x step-by-step with detailed solutions. This problem involves fractions and division of fractions, suitable for Grades 7-9.

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