Reducing
Simplify the expression \(\frac{9x^2 - 16}{3x-4}\)
Cancelling the Common Factors
Simplify the rational expression: \(\frac{9x^2 - 16}{3x + 4}\)
Rewriting in Standard Form
Rewrite the rational expression \(\frac{2x^2 - 5x - 3}{x^2 - 4}\) in standard form.
Operations on Rational Expressions
$\frac{x+\frac{1}{2}}{2+\frac{1}{x}}=$
Determining if the Point is a Solution
Is the point (3, -2) a solution to the equation \(y=\frac{2x-5}{x+1}\)?
Finding the Domain
RATIONAL EXPRESSIONS Restriction on a variable in a denominator: Quadratic
Find all excluded values for the expression.
That is, find all values of $x$ for which the expression is undefined.
\[
\frac{x^{2}-6 x+8}{x^{2}-1}
\]
If there is more than one value, separate them with commas.
\[
x=
\]
Solving over the Interval
Solve the equation \(\frac{3}{x-2} - \frac{2}{x+3} = 1\) over the interval \([-5, 4]\)
Finding the Domain and Range
Find the domain and range of the function \(f(x) = \frac{1}{x+3}\)
Solving Rational Equations
$\frac{x}{(x+2)(x-2)}+\frac{4}{x-2}=\frac{3}{x+2}$
Adding Rational Expressions
$\frac{5}{a^{2}+12 a+36}+\frac{8}{a^{2}-36}$
Subtracting Rational Expressions
$\frac{6 n}{n^{2}-9}-\frac{3}{n+3}$
Multiplying Rational Expressions
Multiply the following rational expr
\[
\frac{x^{2}+2 x-15}{x^{2}+(-4) x-12} \cdot \frac{x^{2}+8 x+12}{x^{2}-9}
\]
Finding the Equation Given the Roots
Use the rational zeros theorem to list all possible zeros of the function $f(x)=7 x^{3}-3 x^{2}-x+2$ Enter the possible zeros separated by commas. You do not need to factor the polynomial.
Finding the Asymptotes
$f(x)=\frac{x-1}{x^{2}-1}$
Finding the Constant of Variation
If \(y = kx^2\), where \(k\) is a constant, and \(y = 25\) when \(x = 5\), what is the value of \(k\)?
Finding the Equation of Variation
If y varies directly as the square of x and inversely as the cube root of z, where y = 9 when x = 3 and z = 8, find the equation of variation.