🧮 algebra

1. **State the problem:** Simplify the expression $\frac{X}{2x^2 - 1}$. 2. **Identify the expression:** The numerator is $X$ and the denominator is $2x^2 - 1$.

1. We are asked to find the value of the function $F$ at $x = -\frac{1}{2}$. However, the function $F(x)$ is not given in the problem statement. 2. To evaluate $F\left(-\frac{1}{2}

1. **State the problem:** Simplify the expression $$\left(\frac{5}{6}\right)^2 \times (-36) + \frac{5}{7} \div \left(-\frac{25}{14}\right)$$. 2. **Recall the rules:**

1. **Problem:** Wandle den Term (−x + 3y)² mithilfe der binomischen Formeln in eine Summe um. 2. **Formel:** Die zweite binomische Formel lautet $$ (a - b)^2 = a^2 - 2ab + b^2 $$

1. **State the problem:** Simplify the expression $$\frac{ab^5 c^0}{a^0 b^{-1} c \cdot a^9 b^{-1} c}$$. 2. **Recall exponent rules:**

1. **State the problem:** Solve the inequality $$\ln(x-2) + \ln\left(\frac{x}{3}\right) \le 0$$ for $x$. 2. **Use logarithm properties:** Recall that $$\ln(a) + \ln(b) = \ln(ab)$$

1. **State the problem:** Simplify the expression $$bc^2 \cdot b^0 c^{-3} \cdot b^{-2} c$$ and express the answer using positive exponents. 2. **Recall exponent rules:**

1. The problem asks to identify two equations that represent the relationship between $x$ (camel rides) and $y$ (elephant rides). 2. The first type of equation is a linear equation

1. The problem asks to identify which equations represent the relationship between $x$ (camel rides) and $y$ (elephant rides) given the options. 2. Typically, such problems involve

1. Das Problem besteht darin, zu zeigen, dass die in Definition 11.1.2 von Reiss und Schmieder definierten Rechenoperationen sowohl assoziativ als auch kommutativ sind. 2. Zuerst e

1. **State the problem:** Solve the inequality $\log_{\frac{1}{2}}(x-3) > 1$. 2. **Recall the logarithm inequality rule:** For a base $b$ where $0 < b < 1$, the logarithm function

1. **State the problem:** Divide the polynomial $2x^{3}+3x^{2}+5x-8$ by $x^{2}+2x+3$. 2. **Recall the division formula:** Polynomial division is similar to long division with numbe

1. **State the problem:** Simplify the expression $$4 \sqrt[3]{81} - 2 \sqrt[3]{72} - \sqrt[3]{24}$$ by reducing each radical and then combining like terms. 2. **Recall the propert

1. Planteamos el problema: Resolver la ecuación $$2 - (-5x + 7) + 2(3x + 2) = 10x$$. 2. Aplicamos la propiedad distributiva y eliminamos paréntesis:

1. **State the problem:** Akeem runs 1 mile each day for 7 days. His times for the first 6 days are 9.4, 9.0, 9.1, 8.9, 8.5, and 8.8 minutes. He wants his average running time over

1. The problem is to find the relationship between the number of seed packages $n$ and the total amount Andres spends $g$ in dollars. 2. From the data given:

1. Das Problem lautet: Löse die Gleichung $2x + 3 = 11$.\n\n2. Die allgemeine Formel zum Lösen linearer Gleichungen der Form $ax + b = c$ ist: $$x = \frac{c - b}{a}$$\n\n3. Wende d

1. Problem: Simplify the expression $\left(2x^3 y^{-3}\right)^{-2}$. Formula: When raising a power to another power, multiply the exponents: $\left(a^m\right)^n = a^{m \cdot n}$.

1. Il problema richiede di studiare il segno della funzione $$f(x) = \frac{x^3}{x^2 + 3}$$. 2. Per studiare il segno di una frazione, dobbiamo analizzare il segno del numeratore e

1. **State the problem:** We are given two numbers whose sum is 9067 and their difference is 6523. We need to find the smaller number. 2. **Set variables:** Let the two numbers be

1. The problem is to understand what you need to know about factoring algebraic expressions. 2. Factoring is rewriting expressions as products of simpler expressions.