🧮 algebra

1. Planteamos el problema: Simplificar la expresión $$\left(\frac{x^{2} - 4}{x^{2} - 5x + 6} + \frac{3x}{x^{2} - 9}\right) \div \left(\frac{x}{x-3} - \frac{2}{x+3}\right) \cdot \le

1. **State the problem:** We are given the ages of Amy, Ray, Clementine, and Jacob in the ratio 8 : 2 : 7 : 3, and their total age sum is 80 years. We need to find Clementine's age

1. **State the problem:** Simplify the expression $$\frac{1}{2x - 6} + \frac{x^2 + 4x + 3}{x^2 + 2x - 15} + \frac{1}{x + 5}$$. 2. **Factor all denominators and numerators where pos

1. Planteamos el problema: sumar las fracciones algebraicas $$\frac{1}{2x - 6} + \frac{x^2 + 4x + 3}{x^2 + 2x - 15} + \frac{1}{x + 5}$$

1. **State the problem:** Calculate the distance between the points $N=(-4,-3)$ and $F=(4,3)$ in the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_

1. **State the problem:** We need to fill in the values of $y$ in the table using the function rule $$y = -10x - 3$$ for the given $x$ values: $-1$, $0$, $1$, and $5$. 2. **Formula

1. Planteamos el problema: Encontrar la ecuación de la recta que pasa por el punto $P(2,-4)$ y tiene pendiente $m=-3$. 2. Usamos la fórmula de la recta en forma punto-pendiente:

1. **State the problem:** Simplify the algebraic expression $$-2y^3 + 0.5x^2y - 12x^2 - 4zy + 3x^3 - 4x^2y - 3x^2 - 4zy + 5y^3 - 3x^2 + 3x^3$$. 2. **Group like terms:** Group terms

1. **Problem Statement:** Given matrices $$A=\begin{pmatrix}-1 & 2 \\ 3 & -4\end{pmatrix}, B=\begin{pmatrix}2 & -3 \\ 0 & 1\end{pmatrix}, C=\begin{pmatrix}2 \\ -3\end{pmatrix}$$

1. Das Problem ist nicht klar formuliert, aber das Wort "Einfacher" deutet darauf hin, dass eine Vereinfachung gewünscht ist. 2. Um einen Ausdruck zu vereinfachen, identifizieren w

1. **Problem statement:** Given the parabola $$y = -3(x + 1.5)^2 + 1$$, find the equations of the parabola after reflection about the colored axes: the blue axis $$y = -1$$ and the

1. **State the problem:** Simplify the algebraic expression $$7xy - 5x^2 - 6y + 2x + 5xy - 3x - 13zy + 3x^3 + 4y - 5x^2 - 4zy + 5x^3$$. 2. **Group like terms:** Combine terms with

1. **Stating the problem:** We are given two equations involving terms with $p_1^3$ and $p_2^3$, and we want to multiply Equation (i) by $b$ and Equation (ii) by $c$, then subtract

1. **Problem statement:** Given rational numbers $a,b,c,p$ with $p$ not a perfect cube, prove that if $$a + b p^{\frac{1}{3}} + c p^{\frac{2}{3}} = 0,$$ then $a = b = c = 0$. 2. **

1. **State the problem:** Solve the equation $$\sqrt{x-1} = x - 5$$ for $x$. 2. **Recall the formula and rules:** To solve equations involving square roots, we isolate the square r

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. Énoncé du problème : Soient $x$ et $y$ des réels tels que $x \leq y$. Complétons les inégalités suivantes avec $\leq$ ou $\geq$. 2. Rappel de règle importante :

1. **Problem statement:** Mr. Old Mac Donald wants to build three fences numbered 1, 2, and 3 around a green square grass carpet that measures 2 meters by 2 meters. We need to calc

1. The problem asks to evaluate the expressions \(\frac{4.12 + 6.71}{8.76 - 8.76}\) and \(\frac{0.13 - 0.13}{100 - 100}\). 2. The formula used is division of sums and differences:

1. **Stating the problem:** We need to check if the given equations are written correctly. 2. **Equation a:** $15 - 6 = 15 + 6$

1. **State the problem:** We have a number line with points 0, ?, 1/2, and 1, and an arrow moving left by 1/7. We want to express the movement and positions using a common denomina