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You've uploaded an image containing several mathematical expressions involving square roots and fractions. I will provide solutions for each expression step by step.

### Expressions:
1. **f.** \( \frac{100}{4\sqrt{10} \div 4} \)
2. **g.** \( \frac{2 - \sqrt{3}}{10} \)
3. **h.** \( \frac{\sqrt{13} + \sqrt{8}}{\sqrt{5}} \)
4. **i.** \( \frac{\sqrt{5} - \sqrt{3}}{\sqrt{8} - \sqrt{5}} \)
5. **j.** \( \frac{\sqrt{8} - \sqrt{5}}{\sqrt{8} + \sqrt{5}} \)

I'll start with the solution to the first expression (f.) and proceed through each one.

---

### Solution to (f)
The expression is:
\[
\frac{100}{4\sqrt{10} \div 4}
\]

First, simplify the denominator:
- \( 4\sqrt{10} \div 4 = \sqrt{10} \)

Now, the expression becomes:
\[
\frac{100}{\sqrt{10}}
\]

Next, rationalize the denominator by multiplying both numerator and denominator by \( \sqrt{10} \):
\[
\frac{100}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{100\sqrt{10}}{10} = 10\sqrt{10}
\]

So, the simplified answer is:
\[
10\sqrt{10}
\]

---

I'll now proceed with solving the next ones. Let me know if you'd like to see detailed steps for each of them, or if you have any questions about this first part.

Solve the following expressions involving square roots and fractions: f. 100 / (4√10 ÷ 4), g. (2 - √3) / 10, h. (√13 + √8) / √5, i. (√5 - √3) / (√8 - √5), j. (√8 - √5) / (√8 + √5).

Solve expressions involving radical fractions, including steps on rationalizing denominators and simplifying square roots. Covers algebraic techniques suitable for Grades 9-11.

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