The algebraic expression (6 x+6)/(x+1) cannot have the same value when two different replacement

step 1 problem, we're being asked to determine if the given equation is true or false. So they want us

The algebraic expression (6 x+6)/(x+1) cannot have the same...

The algebraic expression $\frac{6 x+6}{x+1}$ cannot have the same value when two different replacements are made for $x$ such as $x=-3$ and $x=2$
The value of $\frac{|3-7|-2^{3}}{(-2)(-3)}$ is the fraction that results when $\frac{1}{3}$ is subtracted from $-\frac{1}{3}$

Key Concepts

Fraction Operations

Operations with fractions, including addition, subtraction, multiplication, and division, are central to algebra. Mastery of fraction arithmetic ensures that complex expressions can be simplified and correctly evaluated.

Exponentiation

Exponentiation involves raising a number to a specified power, which is a basic arithmetic operation that appears throughout algebra. Understanding how to correctly compute and simplify expressions with exponents is essential for solving a wide range of mathematical problems.

Order of Operations

The order of operations is a fundamental principle in mathematics that defines the sequence in which operations should be performed to evaluate an expression correctly. This concept prevents ambiguity and ensures consistency when simplifying or solving algebraic expressions.

Domain Restrictions

Domain restrictions refer to the values that a variable in an algebraic expression is not allowed to take, often due to divisions by zero. In any rational expression, identifying and excluding values that make the denominator zero is crucial so that the expression remains defined.

Rational Expressions

Rational expressions are fractions in which both the numerator and the denominator are polynomials. They require careful handling, especially with respect to factorization and cancellation, but only when the factors being cancelled are not zero. This concept is fundamental to algebra and aids in understanding how different substitutions can affect the value of the expression.

Absolute Value

The absolute value function returns the non-negative magnitude of a number regardless of its sign. It is a key concept in algebra and analysis, as it helps in measuring distance and in simplifying expressions that involve both positive and negative numbers.

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