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# System prepended metadata

title: Sample midterm exam B

---

**Problem 1**
Perform the following operation by combining the fractional expressions.

$$
\frac{5x - 7}{x - 1} + \frac{4x + 7}{x + 1}
$$

**Problem 2**
Solve the following equation over the set of real numbers.

$$
-6 - \frac{7x + 5}{3} = -2x - 5
$$

**Problem 3**
Determine the solution of the following system of equations.

$$
\begin{cases}
-8x = - 2y - 54\\
-6x = y - 23
\end{cases}
$$

**Problem 4**
Determine the largest possible domain of the function given by the following formula in interval notation.

$$
f(x)=\sqrt{\,2x+4\,}
$$

**Problem 5**
Simplify the following expression by rationalizing the denominator.

$$
\frac{60}{\sqrt{7}+\sqrt{17}}
$$

**Problem 6**
Solve the following equation over the set of real numbers.

$$
9^{9x - 4} \cdot 9^{x + 8} = 9^{84}
$$

**Problem 7**
Graph the function given by the following formula and determine its largest possible domain and range in interval notation.

$$
f(x) = -2\sqrt{x + 1}
$$

**Problem 8**
The 3rd term of a geometric sequence is 12, and the 7th term is 192. The common ratio of the sequence is a positive number. What is the first term of the sequence?

**Problem 9**
The equation of a circle is $x^{2} + 16x + y^{2} + 18y + 136 = 0$. 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**
One side of a triangle has length $a = 13$ cm and forms angles of $1^\circ$ and $23^\circ$ with its adjacent sides. How long is the longest side of the triangle?


