🧮 algebra

1. The problem is to simplify the expression $$\frac{2x^2 - 18}{8x - 24}$$. 2. First, factor the numerator and denominator.

1. State the problem: Simplify the expression $$\frac{3x^2 - 13x + 4}{3x - 1}$$. 2. Factor the numerator: Find two numbers that multiply to $3 \times 4 = 12$ and add to $-13$. Thes

1. **State the problem:** Simplify the expression $$\frac{8x - 56}{x^2 - 7x}$$. 2. **Factor the numerator:**

1. The problem is to simplify the expression $$\frac{2}{36x + 72}$$. 2. First, factor the denominator: $$36x + 72 = 36(x + 2)$$.

1. The problem states that $f$ and $g$ are polynomial functions. 2. The domain of $\frac{f}{g}$ is $\mathbb{R} - \{3\}$, meaning $g(x) \neq 0$ for all $x \neq 3$, and $g(3) = 0$.

1. **State the problem:** Simplify the expression $$\frac{x + 1}{1 + x}$$. 2. **Analyze the expression:** Notice that the numerator is $x + 1$ and the denominator is $1 + x$.

1. The problem involves simplifying algebraic expressions by combining like terms. 2. Consider the expression: $3x + 2 + 10 + 4x$.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{\sqrt[7]{x - 1 + 3}}{\sqrt{x - 1 + 3}}.$$\n\n2. **Simplify the expression inside the roots:**\n$$x - 1 + 3

1. **Problem 1:** Calculate the value of the expression $$6.285 \times 6.439 \div 8.96 \times 2.764 \div 2$$. 2. Perform the multiplications and divisions step-by-step:

1. The problem is to add unlike fractions, which means fractions with different denominators. 2. To add fractions with unlike denominators, first find the least common denominator

1. **State the problem:** Find the equation of the line passing through the points $(-3,5)$ and $(7,-1)$.\n\n2. **Calculate the slope $m$:** The slope formula is $$m=\frac{y_2 - y_

1. The phrase "from y to x" is ambiguous in a mathematical context and needs clarification. 2. If you mean to express a function or transformation from variable $y$ to variable $x$

1. The problem asks to identify which expression is a like radical to $\sqrt[3]{7x}$. 2. Like radicals have the same index and the same radicand (the expression inside the radical)

1. The problem is to multiply the fractions $\frac{31}{2}$ and $\frac{31}{3}$.\n\n2. To multiply fractions, multiply the numerators together and the denominators together.\n\n3. Mu

1. **State the problem:** We need to simplify the sum $$4 \sqrt[5]{x^{2}y} + 3 \sqrt[5]{x^{2}y}$$. 2. **Identify like terms:** Both terms have the same radical part $$\sqrt[5]{x^{2

1. The problem asks to find which expression is a like radical to $$\sqrt[3]{6x^2}$$. 2. Like radicals have the same radicand (the expression inside the radical).

1. The problem asks to simplify the sum: $$5(\sqrt[3]{x}) + 9(\sqrt[3]{x})$$. 2. Both terms have the same radical part, which is the cube root of $x$, written as $\sqrt[3]{x}$.

1. **State the problem:** Simplify the expression $$7\sqrt[3]{2x} - 3\sqrt[3]{16x} - 3\sqrt[3]{8x}$$. 2. **Rewrite cube roots with prime factors:**

1. **State the problem:** We need to find the value of $x$ such that $3 \times 9^{4x} = 27^{-x}$. 2. **Rewrite the bases as powers of 3:**

1. The problem is to simplify the expression $29^{-2} \times 39^{4}$. 2. Recall that a negative exponent means the reciprocal: $a^{-n} = \frac{1}{a^n}$.

1. The problem is to find the domain of the function $$g(t) = \frac{1}{|t|}$$. 2. The domain of a function is the set of all input values ($t$) for which the function is defined.