🧮 algebra

1. **Stating the problem:** We need to evaluate the expression:

1. **State the problem:** We are given several fractions and asked to analyze their equivalence. The reference fraction is $$\frac{4x - 28}{6x - 42}$$ and the other fractions are $

1. **State the problem:** Simplify the expression $$\frac{21y + 28}{15y^2 + 20y}$$. 2. **Factor numerator and denominator:**

1. **State the problem:** Simplify the fraction $$\frac{(3p)^2}{72pr}$$. 2. **Apply the exponent:** Recall that $ (ab)^2 = a^2 b^2 $. So,

1. **Stating the problem:** Calculate the value of

1. **State the problem:** Simplify the expression $$\frac{8m^2 + 4m}{7(2m + 1)}$$. 2. **Identify the formula and rules:** We want to simplify a rational expression by factoring and

1. **State the problem:** Simplify the expression $$\frac{27h^2}{3h^9(11k + 6)}$$. 2. **Recall the rules:**

1. **State the problem:** We have a total of $12c + 36$ raffle tickets, and among them, $7c + 21$ are winning tickets. We want to find the probability of picking a winning ticket a

1. The problem is to solve the equation or expression given by the user, but since no specific equation was provided, I will demonstrate solving a simple algebraic equation as an e

1. **State the problem:** Simplify the expression $$\frac{6c(4u + 5)}{18c}$$. 2. **Identify the formula and rules:** We can simplify fractions by factoring and canceling common ter

1. **State the problem:** Simplify the expression $$\frac{2r - 14}{6r - 42}$$ fully. 2. **Identify the formula and rules:** To simplify a rational expression, factor both numerator

1. **Problem:** Find the sum of the first 4 terms $S_4$ of a geometric progression where the first term $b_1=4$ and the common ratio $q=\frac{1}{2}$. 2. **Formula:** The sum of the

1. The problem is to understand and analyze the function $y = x - 2$. 2. This is a linear function where $y$ depends on $x$ by subtracting 2 from $x$.

1. **State the problem:** Simplify the expression $$[3x+5y+6z]-[2x+3y+3z]-x-y+2z$$. 2. **Apply the distributive property:** Remove the brackets by distributing the minus signs.

1. **State the problem:** Express the quadratic polynomial $2x^2 + 8x + 6$ in complete square form. 2. **Recall the formula:** A quadratic $ax^2 + bx + c$ can be written as $a(x -

1. **State the problem:** We need to solve the equation $$\frac{5 \times 10^{-8} \times 2}{3 \times 20} = 15.8$$ for verification or simplification. 2. **Write the formula and simp

1. The problem is to find the value of the expression $\{-15,3\} + [\sqrt{20}] - \left[\frac{10}{3}\right] + \{8,3\}$. 2. First, clarify the notation: $\{a,b\}$ means the decimal n

1. **State the problem:** We know that $y$ is inversely proportional to $x$, which means $y \propto \frac{1}{x}$. Given $x=5$ when $y=6$, find $x$ when $y=12$. 2. **Formula and exp

1. Énoncé du problème : Calculer et simplifier les divisions de fractions suivantes, puis vérifier avec une calculatrice. 2. Rappel de la règle : Diviser par une fraction revient à

1. **Stating the problem:** We are given the function $$y = c_1 e^{-2x} + c_2 e^{3x}$$ and want to understand its behavior and graph. 2. **Formula and explanation:** This function

1. The problem is to simplify the expression $14b$. 2. Since $14b$ is already in its simplest form, it represents the product of the number 14 and the variable $b$.