🧮 algebra

1. The problem involves simplifying the expression $\frac{x+3}{5x+4}$ and solving the equation $x^{1}-1=0$. 2. For the expression $\frac{x+3}{5x+4}$, note that it is a rational exp

1. Let's clarify the problem first: we need to determine if the final answer is indeed $\frac{1}{3}$. 2. Without the original problem statement, let's consider a common scenario wh

1. The problem is to understand why a function or graph appears symmetric in the 1st and 3rd quadrants, which is unusual since typical symmetries are about the y-axis, x-axis, or o

1. **State the problem:** Simplify the expression $\frac{x^2 - 9}{5x^2 - 11x - 12}$.\n\n2. **Recall the formula and rules:** To simplify a rational expression, factor numerator and

1. The problem is to simplify the given expression even more. 2. To simplify an expression, we look for common factors, combine like terms, and reduce fractions if possible.

1. **State the problem:** Simplify the expression $\frac{x^2 - 9}{5x^2 - 11x - 12}$. 2. **Factor numerator and denominator:**

1. مسئله را بیان می‌کنیم: حاصل‌جمع پنج عدد طبیعی متوالی برابر با حاصل‌جمع سه عدد متوالی بعدی است. باید بزرگ‌ترین عدد از این هشت عدد را پیدا کنیم. 2. فرض کنیم اولین عدد از پنج عدد م

1. **Stating the problem:** You want to fill columns KOLOM 1 to KOLOM 4 with random values such that the average (rata-rata) column matches the given values.

1. Állítsuk fel a feladatot: szorzattá kell alakítani egy kifejezést kiemeléssel, majd egyszerűsíteni a törtet. 2. Tegyük fel, hogy a kifejezés például $$\frac{x^2 - 9}{x^2 - 6x +

1. Állítsuk fel a feladatot: egyszerűsítsük az alábbi törtet: $$\frac{15x^2 - 21x}{5x(5x - 7)}$$

1. The problem: Understand the Binomial Theorem in a simple way. 2. The Binomial Theorem helps us expand expressions like $$(a+b)^n$$ without multiplying the whole thing repeatedly

1. **State the problem:** Find all the cube roots of $-125$. 2. **Recall the formula:** The cube roots of a number $z$ can be found using the polar form and De Moivre's theorem. Fo

1. **State the problem:** Find all functions $f:\mathbb{R} \to \mathbb{R}$ such that for every $x,y \in \mathbb{R}$, the equation $$1 + f(xy) = f(x + f(y)) + (y - 1)f(x - 1)$$

1. **Problem:** Find the cube root of each of the following numbers: 0, 27, 729, 1728, 6859, and \(\left(\frac{1}{2}\right)^3\). 2. **Formula:** The cube root of a number \(a\) is

1. **Problem Statement:** Find the difference between the temperatures of Lahore and Muree. 2. **Given:** Temperature of Lahore = 24°C, Temperature of Muree = -10°C.

1. **State the problem:** Calculate the total gross income in PHP for a 5-day/4-night group tour to Israel for six adults, given airfare, hotel, and ancillary service costs with ag

1. **State the problem:** Calculate the total gross income in PHP for a 5-day/4-night group tour to Israel for six adults, given airfare, hotel, and ancillary service costs with ag

1. **State the problem:** Simplify the expression $$[(24 - 6) \div 3 - 5] \times (-2)$$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **Problem Statement:** Solve for $x$ in the equation $8x + 4 = 3(x - 1) + 7$. 2. **Formula and Rules:** To solve linear equations, we use the rule of balancing both sides by per

1. **State the problem:** We want to solve the equation $$\sin(0.5t) + 0.3t = 1$$ for $$0 \leq t \leq 1$$. 2. **Understand the equation:** This is a transcendental equation involvi

1. Simplify the expression $x^3 \cdot x^{-5}$. 2. Simplify the expression $\frac{m^{-4}}{m^{-2}}$.