Simplify the rational expression $\frac{x^2-9}{x^2-6x+9}$ and state any domain restrictions.

Simplify the multi-step expression to lowest terms: $(\frac{2x}{3y}÷\frac{4x^2}{9y^3})\cdot \frac{27y}{8x}$

Given $\frac{x^2-1}{x^2-x}$, simplify and state all values of $x$ that are excluded from the domain of the original expression.

Given denominators $12x^2$ and $18x^3$, which of the following is the least common denominator?

Combine and fully simplify: $\frac{2x}{x^2-9}+\frac{3}{x+3}$

Solve for $x$:

$\frac{5}{x^2-9}+\frac{1}{6}=\frac{1}{x-3}$

Solve the system .

Solve $\mid x+1\mid =\mid 2x-3\mid$.

Solve and give the solution in interval notation.

Given the system of constraints $x\ge 0$, $y\ge 0$, $x+2y\le 8$ and $y\ge x-1$, determine whether the point $(3,2)$ is in the feasible region that satisfies all constraints.

A company makes two products: $A$ and $B$. Each product $A$ gives \(30 in profit and uses 2 hours of labor; each product $B$ gives \)50 in profit and uses 3 hours of labor. The weekly labor available is at most 60 hours per week. They must make at least 5 units of product $A$. There is no minimum for $B$. Set up a system of inequalities and determine which corner of the feasible region (integer or fractional that is allowed) that will maximizes the profit: $P=30A+50B$. Show all calculations.

Find the domain of $y=\sqrt{\frac{x+1}{x-2}}$. Express your answer in interval notation.

A linear function $f$ is known to satisfy $f\left(1\right)=3$ and $f\left(3\right)=7$. Find the constants $a$ and $b$ so that $f\left(x\right)=ax+b$.

Explain why f(x) = ∛x has domain all real numbers while f(x) = √x does not. Which mathematical property accounts for this difference?

Let $f\left(x\right)=\frac{1}{x-2}$ and $g\left(x\right)=\sqrt{x}$. Find the domain of $(f\circ g)\left(x\right)$ expressed in interval notation.

A gardener finds that the required fertilizer mass $y$, in units of $\text{kg}$, will vary directly with the garden area $A$, in units of $\text{m}{}^2$, and will vary inversely with the fertilizer concentration $c$, in units of $\frac{\text{kg}}{{\text{m}}^2}$ (for the recommended strength), such that $y=\frac{kA}{c}$. If the gardener uses 50 $\text{kg}$ of fertilizer for a 200 ${\text{m}}^2$ plot with a concentration of $c=2$, determine how many kilograms will be needed for a 300 ${\text{m}}^2$ plot at concentration of $c=3$.

Simplify the expression to its simplest radical form: $\sqrt[3]{864}$

Simplify $\sqrt{\frac{50x^7}{2x^2}}$.

Simplify $\sqrt[3]{432}$ completely by using prime factorization and extracting perfect cubes.