🧮 algebra

1. Bài toán yêu cầu xác định số đường tiệm cận của hàm số $$y=\frac{x+1}{x-1}$$. 2. Hàm số dạng phân thức hữu tỉ có dạng $$\frac{P(x)}{Q(x)}$$, trong đó $P(x)$ và $Q(x)$ là đa thức

1. The problem asks to find the sum of the series \( \sum_{j=15}^{51} \frac{1}{j} \) with an increment of 2 in the index. 2. This means we sum the terms \( \frac{1}{15} + \frac{1}{

1. The problem asks to find the sum of the series $$\sum_{i=15}^{51} \frac{1}{i}$$ with $i$ increasing by 2 each step. 2. This is a finite sum of the reciprocals of odd integers st

1. Problem: If $f$ and $g$ are real functions with $f(x)=\frac{x-2}{x^2-3x+2}$ and $g(x)=x-3$, find $(f/g)(3)$. 2. Formula and rule: The quotient of two functions is given by $(f/g

1. Problem: Determine the domain of the function $f(x)=\sqrt{x-1}+\sqrt{x+2}$. 2. Formula and rules: For a real square root $\sqrt{A}$ to be defined we require $A\ge 0$.

1. Problem statement: Determine the domain of the function $f(x)=\sqrt{\frac{x-3}{\sqrt{5-x}}}$. 2. Condition 1: The expression under the outer square root must be nonnegative, so

1. The problem asks for the domain of the function $f(x) = 5$. 2. The domain of a function is the set of all possible input values ($x$) for which the function is defined.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{5+2x}{x^2 + x + 1}$$. 2. **Recall the domain rule for rational functions:** The domain includes all real nu

1. **Problem statement:** Given that $f(\sqrt{x}) = x^2$, find the value of $f(2)$. 2. **Understanding the problem:** We know the function $f$ is defined such that when its input i

1. The problem asks for the domain of the function $A = \pi x^2$, where $A$ is the area of a circle and $x$ is the radius. 2. The formula for the area of a circle is $A = \pi r^2$,

1. The problem states that the domain of the function $f(x) = \frac{1}{\sqrt{x^2 + a}}$ is $\mathbb{R} - [-5,5]$, meaning the function is undefined for $x$ in the interval $[-5,5]$

1. Problema: Un biciclist a parcurs distanţa dintre două puncte turistice în trei zile cu condiţiile date. 2. Notăm cu $x$ lungimea întregului traseu turistic.

1. We are given positive real numbers $a,b,c,d$ such that $a+b+c+d=11$ and want to find the value of $\beta$ if the maximum of $a^5 b^3 c^2 d$ is $3750 \beta$. 2. To maximize the p

1. **Problem Statement:** We are given a number line with open circles at $-5$ and $-2$, and a solid line segment connecting these points, indicating the inequality $-5 < x < -2$.

1. **Problem statement:** Simplify the algebraic expressions given. 2. **Recall the rule:** To simplify expressions, combine like terms. Like terms have the same variable raised to

1. **State the problem:** Simplify the algebraic expressions: a) $4a + 7b + 5a - b$

1. The problem is to simplify the algebraic expression $4n + 7m + 3n - m$. 2. To simplify, combine like terms. Like terms are terms that have the same variable raised to the same p

1. **Stating the problem:** A letter costs Le 300 for the first gram and Le 50 for each additional half gram or part thereof. We need to find the total cost to post a letter weighi

1. **State the problem:** A woman uses 1 pint of nut oil to 8 pints of water. She increases the quantity by 50%. We need to find how many pints of water she will use now. 2. **Unde

1. **State the problem:** We need to find what percentage of the total school population entered for the Basic Certificate Education Examination. 2. **Identify the given values:**

1. **State the problem:** Simplify the expression $$\left( \frac{4}{5} + \frac{2}{3} \right) - \left( \frac{1}{3} \right)^2$$. 2. **Recall the formula and rules:** To add fractions