Simplify the rational expression. .

$$\frac{6 y-18}{2 y-6}$$

Simplify the rational expression.

$$\frac{x^2-x-2}{x^2-1}$$

Solve the following system of equations by applying the substitution method :

$$\begin{alignat*}{5} x&-y\ =-&2\\ x^2&+y^2=& 2 \end{alignat*}$$

Underline the word in parentheses that best completes each sentence.

The reason we ate dinner late is (because, that) I had to work until seven.

Solve the following problem using the MATLAB environment. Do not use MATLAB's built-in functions for changing the form of numbers.

Write a user-defined MATLAB function that converts integers written in binary form to decimal form. Name the function $d=$ binaTOint $(b)$, where the input argument $b$ is a vector with 1s and 0s that represents the binary number to be converted and the output argument $d$ is a number in decimal form. The largest number that could be converted with the function should be a binary number with 20 1s. If a larger number is entered for b, the function should display an error message. Use the function to convert the following numbers: (a.) 11010. (b.) 10101100111. (c.) 11100110001110101.

Write the rational number as a decimal.

$$-\frac{21}{16}$$

Evaluate the system by the substitution method.

$$\left\{\begin{array}{l}x^2+y^2=5 \\ 3 x-y=5\end{array}\right.$$

Find the domain of the given rational function.

$$f(x)=\frac{x+2}{x^2+x-2}$$

Solve each exponential equation for $x$ to three decimal places.

$$4^{x+2}=5^{x+7}$$

Tell whether the number is rational or irrational. √(16//5)

Write the rational number as a decimal.

$$\frac{3}{11}$$

Write the rational number as a decimal.

$$-2 \frac{17}{18}$$

Find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function.

$$g ( x ) = \frac { 2 x - 4 } { x + 3 }$$

Find the domain of each rational expression.

$$\dfrac{x+3}{x-6}$$