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.