🧮 algebra

1. **State the problem:** Solve the equation $$\frac{X - 1}{X} - 2 = \frac{-X - 1}{X^2 - 2X}$$ for $X$. 2. **Rewrite the equation:** Note that $X^2 - 2X = X(X - 2)$, so the equatio

1. **State the problem:** Simplify the expression $4151 + 3\sqrt{6}$. 2. **Understand the terms:** The expression consists of a whole number $4151$ and a term with a square root $3

1. **State the problem:** Simplify the expression $$6v^2 \cdot \left( \frac{9u}{v} \right)^7 \cdot \left( \frac{v}{3u} \right)^{-2} \div \left( \frac{9u}{v} \right)^9$$. 2. **Recal

1. **State the problem:** Simplify the expression $$6v^2 \cdot \left(\frac{9u}{v}\right)^7 \cdot \left(\frac{v}{3u}\right)^{-2} \div \left(\frac{9u}{v}\right)^9$$. 2. **Recall the

1. **State the problem:** We need to find the area of a rectangular animal pen with a total fencing length of 200 meters, where one side is 60 meters. 2. **Formula used:** The peri

1. **State the problem:** We have a building 51 feet tall casting a shadow 48 feet long. A nearby statue casts a shadow 16 feet long. We need to find the height of the statue. 2. *

1. **Stating the problem:** We want to understand the method used to factor expressions like $p^2 - 1^2$ and $25v^2 - 49$ using special algebraic identities. 2. **Formula used:** T

1. The problem is to solve the equation given by the user, but since no specific equation was provided, I will demonstrate solving a simple example equation: $2x + 3 = 7$. 2. The f

1. The user asked for a simpler explanation or solution. 2. Since no specific problem was given, I will provide a simple example of solving a linear equation.

1. **State the problem:** Solve the system of linear equations: $$6x - 4y = 16$$

1. The problem is to find the value of $y$ in the system of linear equations: $$10x - y = 0$$

1. مسئله: دنباله هندسی چیست و چگونه می‌توان جملات آن را پیدا کرد؟ 2. فرمول دنباله هندسی: هر جمله از دنباله هندسی با فرمول $$a_n = a_1 \times r^{n-1}$$ محاسبه می‌شود که در آن:

1. مسئله را بیان می‌کنیم: دو معادله داریم که به صورت دنباله حسابی هستند: $$a_1 + a_5 = 30$$

1. مسئله را بیان می‌کنیم: اگر پیمانه را 11 در نظر بگیریم، باید مسئله را با این مقدار جدید حل کنیم. 2. فرض کنیم مسئله اصلی مربوط به تقسیم یا محاسبه‌ای است که در آن پیمانه نقش دارد.

1. مسئله: هزینه کرایه دوچرخه شامل هزینه ثابت ۲۰۰۰ تومان و هزینه متغیر ۱۵۰۰ تومان به ازای هر ساعت است. می‌خواهیم تابع هزینه را بر حسب ساعت $x$ بنویسیم، هزینه پس از ۳ ساعت را محاسبه

1. The problem is to understand the ratio 20:8 and relate it to 8 cups of pineapple. 2. A ratio compares two quantities, here 20 to 8, which can be simplified by dividing both numb

1. Let's start with the first question: Create a table that shows at least three possible combinations of soda water and pineapple juice to make pineapple soda. The recipe says for

1. **Problem Statement:** Calculate the value of the expression $$|2 - 4 \times 6 \div 3 + \sqrt{1}|$$. 2. **Formula and Rules:** Follow the order of operations (PEMDAS/BODMAS): Pa

1. **State the problem:** Convert the parametric equations $$x = 3 + 2 \sin t$$

1. The problem is to find the solution set of the inequality $$\frac{x-1}{x+2} > 0$$. 2. To solve inequalities involving rational expressions, we find where the numerator and denom

1. **Stating the problem:** The user requests the most detailed step-by-step explanation for a math problem, but no specific problem is given. 2. Since no explicit problem is provi