🧮 algebra

1. **State the problem:** Simplify and verify the equation $$\frac{5}{x+3} + \frac{2}{x-3} = \frac{5}{x^2 - 9}$$ where the denominators are expressions involving $x$. 2. **Recall t

1. **State the problem:** Solve the equation $$\frac{2}{3} + \frac{1}{y} = \frac{1}{5}$$ for $y$. 2. **Isolate the term with $y$:** Subtract $\frac{2}{3}$ from both sides:

1. **State the problem:** Solve the equation $$\frac{2}{3} + \frac{1}{y} = \frac{1}{5}$$ for $y$. 2. **Isolate the term with $y$:** Subtract $\frac{2}{3}$ from both sides:

1. **Problem 19:** Solve the equation $$\sqrt{y - 5} + 5 = y$$ 2. **Step 1:** Isolate the square root term:

1. **Énoncé du problème :** Simplifier les expressions suivantes impliquant des exponentielles et des logarithmes naturels. 2. **Rappel de la formule importante :** Pour tout $x >

1. **State the problem:** Solve the inequality $\ln(x) > 4$. 2. **Recall the definition and properties:** The natural logarithm function $\ln(x)$ is defined for $x > 0$ and is the

1. **Stating the problems:** We need to solve the following equations:

1. **State the problem:** Solve the inequality $|x-2| > 2|x-1|$. 2. **Recall the definition of absolute value:** For any real number $a$, $|a| = a$ if $a \geq 0$, and $|a| = -a$ if

1. **State the problem:** We need to simplify the expression $$(3 - \sqrt{2})(4 + \sqrt{2})$$. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL m

1. **Stating the problem:** We are given the system of equations:

1. **State the problem:** Solve the system of linear equations: $$\begin{cases}x-2y=4\\ 3x+y=9\end{cases}$$

1. **Problem Statement:** We are given a line on a Cartesian plane that crosses the y-axis near $y=6$ and the x-axis near $x=4$. We need to find the slope of this line in simplest

1. **State the problem:** Solve the linear equation $x - 2y = -4$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. This

1. **Problem Statement:** Solve the system of equations derived from the equation $x^2 + y^2 + z^2 = 14$ using the Gaussian elimination method. 2. **Important Note:** Gaussian elim

1. The problem is to find the turning point (vertex) of the parabola given by the equation $y=(x+a)^2 + b$. 2. The general form of a parabola's vertex form is $y=(x-h)^2 + k$, wher

1. **Problem Statement:** Solve the system of quadratic equations: $$\begin{cases} x^2 + y^2 + z^2 = 14 \\ x^2 - y^2 + 2z^2 = 15 \\ x^2 + 2y^2 + 3z^2 = 36 \end{cases}$$

1. **State the problem:** We need to compare the rates of change (slopes) of the data given in the table and the graph. 2. **Rate of change formula:** The rate of change between tw

1. **Problem Statement:** We are given a graph showing the number of cars remaining in a parking lot over time after a baseball game. The vertical axis shows cars in hundreds, and

1. **State the problem:** Evaluate the expression $9 - 3(0)$.\n\n2. **Recall the order of operations:** According to PEMDAS (Parentheses, Exponents, Multiplication and Division, Ad

1. **Énoncé du problème :** Soit $f : \mathbb{R} \setminus \{2\} \to \mathbb{R}$ définie par

1. **State the problem:** Evaluate the expression $9 + 3(-1)$.\n\n2. **Recall the order of operations:** According to the order of operations (PEMDAS/BODMAS), multiplication is per