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Let's solve the three questions one by one.

### 1. If \( x \) equals:
\[
\frac{60}{19} + \frac{1890}{190} + \frac{1890}{100}, \text{ then find the range of } x.
\]
We need to calculate \( x \):
\[
x = \frac{60}{19} + \frac{1890}{190} + \frac{1890}{100}
\]

Let's compute each term:
1. \( \frac{60}{19} \approx 3.16 \)
2. \( \frac{1890}{190} = 9.95 \)
3. \( \frac{1890}{100} = 18.90 \)

Thus, \( x \approx 3.16 + 9.95 + 18.90 = 32.01 \).

The closest range for \( x \) is \( 10 < x < 100 \), so the answer is **(b)**.

---

### 2. The expression:
\[
\frac{1}{\sqrt{5}-1} - \frac{1}{\sqrt{5}+1}
\]
We simplify this by rationalizing the denominators. Start with:
\[
\frac{1}{\sqrt{5} - 1} \cdot \frac{\sqrt{5} + 1}{\sqrt{5} + 1} = \frac{\sqrt{5} + 1}{(\sqrt{5})^2 - 1^2} = \frac{\sqrt{5} + 1}{5 - 1} = \frac{\sqrt{5} + 1}{4}
\]

Now the second term:
\[
\frac{1}{\sqrt{5} + 1} \cdot \frac{\sqrt{5} - 1}{\sqrt{5} - 1} = \frac{\sqrt{5} - 1}{(\sqrt{5})^2 - 1^2} = \frac{\sqrt{5} - 1}{4}
\]

Now subtract:
\[
\frac{\sqrt{5} + 1}{4} - \frac{\sqrt{5} - 1}{4} = \frac{\sqrt{5} + 1 - (\sqrt{5} - 1)}{4} = \frac{\sqrt{5} + 1 - \sqrt{5} + 1}{4} = \frac{2}{4} = \frac{1}{2}
\]

Thus, the answer is **(c) \(\frac{1}{2}\)**.

---

### 3. Multiply:
\[
\frac{2x+1}{x+1} \cdot \frac{3x^2 - 2x}{x^2 - y^2}
\]
Recognize that \( x^2 - y^2 \) is a difference of squares:
\[
x^2 - y^2 = (x - y)(x + y)
\]

So the expression becomes:
\[
\frac{(2x+1)}{(x+1)} \cdot \frac{3x(x - \frac{2}{3})}{(x - y)(x + y)}
\]

After multiplication and simplification, the resulting expression would be:
\[
\frac{3x(2x+1)}{(x+1)(x - y)(x + y)}
\]

Thus, the correct answer is **(b)**.

---

Do you need more details on any of these steps or explanations?

Here are five related questions to further your understanding:
1. How do you simplify expressions with square roots in the denominator?
2. What is the process of rationalizing a denominator?
3. How do you recognize and simplify a difference of squares?
4. How can you quickly estimate the value of fractions like \( \frac{60}{19} \)?
5. Why is it important to check the range of the solution after calculation?

### Tip:
Always simplify the terms step-by-step and keep an eye on common algebraic identities like difference of squares to make calculations easier.

1. If x equals (60/19) + (1890/190) + (1890/100), find the range of x. 2. The expression 1/(√5 - 1) - 1/(√5 + 1) equals? 3. Multiply (2x + 1)/(x + 1) * (3x^2 - 2x)/(x^2 - y^2).

Learn how to solve the expression combining fractions and square roots, rationalizing denominators, and multiplying complex fractions. Suitable for students in Grades 9-12. This problem involves core algebraic concepts such as the difference of squares and rationalizing denominators.

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