🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{2}{x^2 - 2x} - \frac{5}{x^2 + x - 6}$$. 2. **Factor the denominators:**

1. **State the problem:** We need to show that there is no constant term (term independent of $x$) in the expansion of $$\left(3x^8 - \frac{3}{x^{15}}\right)^{10}.$$\n\n2. **Recall

1. The problem asks to find the percentage of a journey completed by walking. 2. To find the percentage, use the formula: $$\text{Percentage} = \left(\frac{\text{Distance walked}}{

1. **Problem:** Simplify the algebraic expression $3a(2a - 3b + 4c)$ correctly. 2. **Formula and rules:** Use the distributive property: $a(b + c) = ab + ac$.

1. **State the problem:** Simplify the expression $1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Simplify the expression $$1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7}$$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Simplify the expression $$\frac{2\frac{1}{2}}{1-\left(\frac{1}{2}\right)^2}$$. 2. **Convert mixed number to improper fraction:**

1. **State the problem:** Simplify the expression $$\frac{-\frac{1}{3}-\left(-3\right)}{1+\left(-\frac{1}{3}\right)\left(-3\right)}$$. 2. **Recall the formula:** This expression re

1. **State the problem:** We need to analyze the function $$f(x) = (x - 1)^3 (x + 2)^2$$. 2. **Formula and rules:** This is a polynomial function expressed as a product of powers o

1. **Enunciado do problema:** Calcular o erro relativo da estimativa por interpolação linear para $x=2,7$ usando os dados da tabela e compará-lo com o valor exato $y=0,993251$.

1. O problema pede para fazer uma interpolação polinomial usando os pontos dados $(-1,1)$, $(1,1)$ e $(3,-7)$ e avaliar o polinômio em $x=0$. 2. Usaremos o método de interpolação p

1. O problema pede para encontrar o valor de $y$ quando $x=0$ usando interpolação polinomial com os pontos dados: $(-1,1)$, $(1,1)$ e $(3,-7)$. 2. Usaremos o polinômio interpolador

1. Vamos considerar o sistema linear dado: $$\begin{cases} x_1 + 8x_2 + 2x_3 = 10 \\ 15x_1 + x_2 + 2x_3 = 13 \\ x_1 + x_2 + 3x_3 = -4 \end{cases}$$

1. O problema pede a solução do sistema de equações: $$\begin{cases} 3x_1 + 5x_2 = 13 \\ 2x_1 + x_2 = 6 \end{cases}$$

1. El problema pide hallar el dominio y rango de cada función dada. 2. Recordemos que el dominio de una función es el conjunto de valores de $x$ para los cuales la función está def

1. **State the problem:** Solve the equation $-3y = 33$ for $y$. 2. **Formula and rules:** To solve for $y$, divide both sides of the equation by $-3$.

1. **State the problem:** Solve for $x$ in the equation $3 \cdot (-2.5) = x$. 2. **Formula and rules:** Multiplication of a positive number by a negative number results in a negati

1. The problem is to write the inequality represented by the graph. 2. The graph shows a solid dot at $-2$ and a line extending to the right up to $4$ and beyond, indicating all nu

1. The problem is to write the inequality represented by the graph. 2. The graph shows a solid dot at 0 and shading extending to the right, indicating all values greater than or eq

1. **State the problem:** Simplify the expression $$4^{\frac{3}{4}} \times \sqrt{\left(\frac{6}{5}\right)^{15} \times \left(\frac{6}{5}\right)^9}$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$\frac{x+2}{3} - \frac{1}{2} = 2$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to eliminat