🧮 algebra

1. Simplify the expression $$\frac{4 - \frac{9}{x^2}}{2 - \frac{3}{x}}$$

1. Énoncé du problème : on cherche à calculer la valeur de l'expression $3x + 7$ pour $x$ allant de 1 à 50. 2. Dans un tableur, on commence par écrire le titre "valeur de x" dans l

1. Let's analyze the given sets of points and try to identify if they represent functions. 2. Recall that in a function, each input (x-value) must correspond to exactly one output

1. **Problem Statement:** Given that $\tan \theta = \frac{a^2 + ab + b^2}{ab}$, show that $\tan \theta > 3$. 2. **Rewrite the expression:** Start with the given expression:

1. The problem involves analyzing the function $$f(x) = \frac{a}{x+r} + t$$ with given information about its symmetry axis $$h(x) = -x + 3$$, points $$C=(0,3)$$ on the axis, and po

1. State the problem: Thirdy bought a cellphone for 15291.50 after a 15% discount. We need to find the original price and the discount amount. 2. Let the original price be $P$.

1. The problem involves graphs of $f(x) = \frac{1}{2}(x+p)^2 + q$ and $g(x) = \frac{a}{x+r} + t$, with axis $h(x) = -x + 3$ symmetrical to $g$, and points labeled as C, E, B among

Solve the following exponential equations and inequalities step-by-step. 1. Solve $4^{3x+1} = 8^{x-1}$:

1. **State the problem:** Solve the equation $24x + 18 - 4x = 21x - 12$ for $x$. 2. **Simplify the left side:** Combine like terms $24x - 4x$ to get $20x$, so the equation becomes:

1. The problem is to evaluate the expression $2^3 + 2^1$. 2. Calculate $2^3$: since $2^3 = 2 \times 2 \times 2 = 8$.

1. The problem is to simplify the expression $$\left(\frac{2}{3}\right)^{-3}$$ and verify that it equals $$\left(\frac{3}{2}\right)^3$$ and $$\frac{27}{8}$$. 2. Start by applying t

1. **Stating the problem:** A school bag is on sale at 15% off, and the sale price is 841.50. We need to find the original price before the discount. 2. **Understanding the discoun

1. The problem involves evaluating two expressions: $(-3)^4$ and $(-2)^3$. 2. First, calculate $(-3)^4$. This means multiplying $-3$ by itself 4 times:

1. The problem is to simplify expressions or equations by eliminating fractions. 2. To remove a fraction from an equation, multiply both sides of the equation by the denominator to

1. First, state the problem: evaluate $8^3 \times 4^{-2}$. 2. Calculate $8^3$: since $8 = 2^3$, then $8^3 = (2^3)^3 = 2^{9} = 512$.

1. The problem is to draw the curve of the function $y=-(x-5)-2$. 2. Start by simplifying the expression inside the function.

1. Let's first clarify the problem statement. You have an expression where the square root applies only to the squared part of it, not the entire expression. 2. For example, if the

1. Let's analyze the sequence given starting from the simple arithmetic statement $1 + 1 = 2$. 2. Next steps attempt to transform or equate $2$ to other expressions such as $4 - 2$

1. State the problem: Simplify the expression $$H = \sqrt{3} - 2\sqrt{2} + \sqrt{\frac{3}{2}} \sqrt{9}$$. 2. Simplify the term $$\sqrt{\frac{3}{2}} \sqrt{9}$$ using the property $$

1. Let $f(x) = x^2 - 1$ and $g(x) = 2x + 3$. Find; (a) $(f \circ g)(x)$ and $(g \circ f)(x)$.

1. Problem a: Given $a^x = b^y = c^z$ and $a, b, c$ are in geometric progression (G.P.), prove that $x, y, z$ are in harmonic progression (H.P.). Step 1: Since $a, b, c$ are in G.P