---

## Problem 1

Perform the following operation by combining the fractional expressions.

$$
\frac{1}{6x - 5y} \;-\; \frac{5}{6x + 5y}
$$

---

## Problem 2

Solve the following equation over the set of real numbers.

$$
9 - 4\left(\frac{x}{7} - 2\right) = -2x - 6
$$

---

## Problem 3

At a market, a customer paid 5200 Ft for 5 kg of potatoes and 4 kg of onions. The next customer paid 2000 Ft for 3 kg of potatoes and 1 kg of onions. How much does 1 kg of potatoes cost, and how much does 1 kg of onions cost?

---

## Problem 4

Determine the largest possible domain of the function given by the following formula in interval notation.

$$
f(x) = \log_{5}(7x - 3)
$$

---

## Problem 5

Simplify the following expression by rationalizing the denominator.

$$
\frac{-24}{\sqrt{2x - 9} - \sqrt{2x + 3}}
$$

---

## Problem 6

Solve the following equation over the set of real numbers.

$$9⁴ˣ⁺⁹ · 9⁻³ˣ⁻⁴ = 9⁹$$

---

## Problem 7

Graph the function given by the following formula and determine its largest possible domain and range in interval notation.

$$ f(x) = -(x + 6)(x + 9)$$

---

## Problem 8

A product was purchased for 6 million HUF. Its value increases by 0.8% every month. How much will the product be worth after 10 months?

---

## Problem 9

The equation of a circle is $x^2 + 10x + y^2 - 6y + 18 = 0$. Transform the equation into a form from which the coordinates of the center and the radius of the circle can be directly read. What is the center of the circle and what is its radius?

---

## Problem 10

The sides of an isosceles triangle are 19 cm long and enclose an angle of 69 degrees. How long is the base of the isosceles triangle?