🧮 algebra

1. **State the problem:** Simplify and solve the equation $$x^2 - x - \frac{x^2 - x + 2}{x^2 + 1} + \frac{x^2}{x - 2} = 1$$ for $x$. 2. **Rewrite the equation:** To solve, get all

1. **State the problem:** We are given the system of linear equations: $$x + y + z = 6$$

1. The given expression is $28xy - 12x$. 2. To simplify, we look for the greatest common factor (GCF) of the terms.

1. **State the problem:** Solve the equation $$\frac{24}{x^2 + 2x - 8} - \frac{15}{x^2 + 2x - 3} = 2$$ for the variable $x$.\n\n2. **Factor the denominators:**\n\- Factor $x^2 + 2x

1. Planteamos el problema: desarrollar la expresión $$\log(z^{3} \sqrt{x^{5} y})$$ usando propiedades logarítmicas, sin radicales ni exponentes dentro del logaritmo. 2. Recordemos

1. The problem asks us to find the cube of a whole fraction. A whole fraction means a fraction where the numerator and denominator are whole numbers. 2. Let's say the fraction is $

**A. Find the perfect cubes of the following numbers.** 1. Calculate $10^3=10 \times 10 \times 10=1000$.

1. Solve $$\frac{2x}{x+6} \geq 1$$ Step 1: Move all terms to one side:

1. The problem is to find the cube of a fraction, which means raising the fraction to the power of 3. 2. Let the fraction be $\frac{a}{b}$, where $a$ is the numerator and $b$ is th

1. We are given a system of two equations with variables $m$ and $n$: $$\frac{m}{2} + \frac{n}{3} - \frac{13}{6} = 0$$

1. Stating the problem: We know the battery was charged from 23% to 89% over 30 minutes.

1. Mari kita nyatakan harga sebuah pensil sebagai $x$. 2. Karena harga sebuah buku adalah 3 kali harga sebuah pensil, maka harga sebuah buku adalah $3x$.

1. **State the problem:** Solve for $b$ in the equation $$2b - 7 = \frac{1}{3}b + 3$$. 2. **Isolate variable terms:** Subtract $\frac{1}{3}b$ from both sides to get all $b$ terms o

1. We are given the function $p(u) = u^3 - 3u^2 + 4u$ with $u$ in meters. The problem involves understanding this cubic function and its interaction with the factor $(u - 2)$, whic

1. The problem is to define the region shaded on the graph which is bounded by the curve $y^2 = 4x$, the line $x=1$, and the x-axis ($y=0$). 2. First, understand the curve. The equ

1. The problem is to factorize the quadratic expression $$x^2 + 5x + 6$$. 2. Start by breaking the middle term into two terms whose coefficients add up to 5 and multiply to 6. Here

1. Solve $5r^2 + 10r = 80$ by completing the square. Step 1: Divide the entire equation by 5 to simplify:

1. Stating the problem: Solve the equation $34 = 4 + 6x$ for $x$. 2. Subtract 4 from both sides to isolate the term with $x$:

1. **State the problem:** Solve the equation $$38 = 10h + 7$$ for $h$. 2. **Isolate the term with $h$:** Subtract 7 from both sides:

1) Calculate the following: &i. Calculate $1^2 - 2^3 \times 3 + 8 \div 4 - (3^3 + 2)$:

1. State the problem: Solve the linear equation $$10.5 = 3x - 1.5$$ for $x$. 2. Add $1.5$ to both sides to isolate the term with $x$: