🧮 algebra

1. The problem is to factorise the numerator of a given expression. 2. To factorise a numerator, we look for common factors or use methods like grouping, difference of squares, or

1. **State the problem:** Simplify the rational function $$\frac{x^2 + x - 6}{x^2 - 7x + 10}$$. 2. **Recall the formula and rules:** To simplify a rational function, factor both nu

1. **State the problem:** Solve the two-step equation $$6x + 12 = 84$$ for $$x$$ where the solution is a positive integer. 2. **Formula and rules:** The general form of a two-step

1. **Problem a:** Löse die Gleichung $$4x + 6 = 7x + 3(2 - x)$$. 2. **Formel und Regeln:** Um lineare Gleichungen zu lösen, bringen wir alle Terme mit $x$ auf eine Seite und die Ko

1. **State the problem:** Simplify the expression $9 \times 9\sqrt{9} \div 4\sqrt{9}$. 2. **Recall the rules:** The square root of 9 is $\sqrt{9} = 3$. Multiplication and division

1. **State the problem:** Calculate the value of the expression $2 \times 4 - 5 \times 58693 - 4$. 2. **Recall the order of operations:** Multiplication and division are performed

1. Representa sin el signo “x” o “·” las siguientes expresiones algebraicas: - a) $15a$

1. **State the problem:** We need to multiply the binomial $(3x + y)$ by the trinomial $(x^2 + 2y + 4)$ and identify the correct terms in the multiplication chart. 2. **Formula and

1. **State the problem:** Find the product of the polynomials $a+3$ and $-2a^2+15a+6b^2$. 2. **Formula and rules:** To multiply polynomials, use the distributive property: multiply

1. **State the problem:** Solve the system of equations and understand their graph shapes: $$x - y + 2 = 0$$

1. **State the problem:** A photograph measures 11 inches wide and 14 inches long. It is enlarged so that the new width is 231 inches. We need to find the new length. 2. **Formula

1. Le problème semble concerner la définition de l'expression $0^0$ et la comparaison avec d'autres expressions comme $0^{1-1}$ ou $\frac{0^1}{0^1}$. 2. En mathématiques, $0^0$ est

1. Énonçons le problème : Pourquoi $0^0 = 1$ alors que $\frac{0}{0}$ n'a pas de valeur définie ? 2. Rappelons que $0^0$ est une forme indéterminée en analyse, mais en algèbre et co

1. **State the problem:** Simplify the expression $$\frac{\frac{(x - 2)^2}{2(x^2 - 5x + 4)}}{\frac{x^2 - 4}{4x - 10}}$$. 2. **Rewrite the complex fraction:** Dividing by a fraction

1. Planteamos el problema: Dado que $\log_{\sqrt[4]{3}} \sqrt[3]{2} = x$, hallar el valor de $$\frac{\log 32}{\log 9}$$. 2. Recordemos que el cambio de base para logaritmos es $$\l

1. **State the problem:** Solve the linear equation $8x + 6 = 22$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ on one side by performing inverse operations. Rem

1. **State the problem:** We need to find the gradient (slope) of the linear equation $8x + 6 = 22$ and represent it in slope-intercept form. 2. **Rewrite the equation:** Start by

1. The problem is to find the gradient of a function or a line. 2. The gradient (or slope) of a line is given by the formula:

1. **State the problem:** Solve the linear equation $8x + 6 = 22$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable $x$ by performing inverse oper

1. **Problem Statement:** We are given two relations:

1. **State the problem:** Calculate the value of the expression $$\frac{328-(120+98)}{22}$$. 2. **Apply the order of operations:** First, solve the expression inside the parenthese