🧮 algebra

1. **Problem 8: Find the removable point of discontinuity (RPOD) for** $f(x) = \frac{x+1}{x^2 - 1}$. 2. **Recall the formula and rules:**

1. **State the problem:** Find the x-intercept(s) of the function $$f(x) = \frac{x+2}{x^2 - 4}$$. 2. **Recall the rule for x-intercepts:** The x-intercept(s) occur where the functi

1. **State the problem:** Find the x-intercept of the function $$f(x) = \frac{x + 2}{x^2 - 4}$$. 2. **Recall the rule for x-intercepts:** The x-intercept occurs where the function

1. **State the problem:** Multiply and simplify the expression assuming $u \geq 0$: $$\sqrt{6u^5} \cdot \sqrt{3u^3} \div \sqrt{3^2} \cdot 2 \cdot (u^2)^4$$

1. **Problem 8: Find the R P O D (Removable Point of Discontinuity) for $f(x) = \frac{x+1}{x^2 - 1}$.** 2. The function is a rational function where the denominator is $x^2 - 1 = (

1. The problem is to understand why 0.0002 might be considered wrong or to clarify its value. 2. The number 0.0002 in decimal form means $2 \times 10^{-4}$.

1. **Problem 7: Find the horizontal asymptote of** $f(x) = \frac{3x^2 + 2x}{x^2 - x - 6}$. 2. **Recall the rule for horizontal asymptotes:**

1. The problem asks: "What goes in the boxes?" which suggests filling in missing values or expressions in a mathematical context. 2. Without additional context or a specific equati

1. **State the problem:** We have three systems of linear equations A, B, and C. We want to find the transformations between these systems. 2. **Analyze System A to System B:**

1. **Problem:** Find the vertical asymptote(s) for the function $$f(x) = \frac{x+2}{x^2 - x - 6}$$. 2. **Recall:** Vertical asymptotes occur where the denominator is zero and the n

1. **State the problem:** Simplify the expression $\frac{5 \times 70 - 50}{10}$. 2. **Apply the order of operations:** First, multiply $5$ by $70$.

1. **State the problem:** Divide the polynomial $$2x^3 - 5x^2 + 3x + 7$$ by the binomial $$x - 2$$. 2. **Formula and method:** Use polynomial long division or synthetic division to

1. The problem is to write an equation. 2. An equation is a mathematical statement that asserts the equality of two expressions, typically written as $A = B$.

1. **State the problem:** We are given the rational function $$f(x) = \frac{x+3}{x^2 + 2x - 3}$$ and asked to analyze and graph it, including finding intercepts, domain, vertical a

1. **State the problem:** Write the equations of the vertical and horizontal lines passing through the point $(-1, -2)$. 2. **Recall the definitions:**

1. **State the problem:** Solve the equation $0.1^{2x-1} = 100$ for $x$. 2. **Recall the formula and rules:** We use the property of exponents and logarithms. Since $0.1 = 10^{-1}$

1. **State the problem:** Simplify the complex fraction $$\frac{\frac{x^2 - 1}{x^2 + x}}{\frac{x - 1}{x + 1}}$$ and find which expression it is equivalent to. 2. **Recall the rule

1. **State the problem:** Solve the equation $-4x^3 - 4x = 0$ for $x$. 2. **Factor the equation:** Factor out the common factor $-4x$:

1. The problem asks for the solution to a system of two linear equations based on their graph. 2. The solution to a system of linear equations is the point where the two lines inte

1. **State the problem:** We need to determine which of the given equations does NOT have $\frac{3}{2}$ as a solution. 2. **Recall the method:** To check if $x=\frac{3}{2}$ is a so

1. **State the problem:** Solve the equation $$\frac{5y}{4} - \frac{y}{2} = -\frac{3}{4}$$ for $y$. 2. **Identify the formula and rules:** To solve for $y$, combine like terms and