Grade 9 LP - Fractional Expressions

Vocabulary and core algebraic rules for Grade 9 LP fractional expressions, factoring, and equation solving.

Fractional Expression

An algebraic expression written as the quotient of two polynomial expressions, in the form $f(x) = \frac{A(x)}{B(x)}$.

Condition of Definition (Domain)

The requirement that a fractional expression $f(x) = \frac{A(x)}{B(x)}$ is defined only for values of $x$ where the denominator is non-zero ($B(x) \neq 0$).

Forbidden Values

The values of $x$ that make the denominator equal to zero ($B(x) = 0$), for which the fractional expression is undefined and which must be excluded from potential solutions.

Initial Factorization Rule

The instruction to factorize the numerator $A(x)$ and denominator $B(x)$ first before simplifying or solving a fractional expression.

Product of Factors of First Degree

An algebraic expression factored completely into linear factors, where the variable in each factor has an exponent of $1$.

Expand, Reduce and Arrange

The algebraic procedure of performing multiplications to remove parentheses (expand), combining like terms (reduce), and writing terms in descending order of their exponents (arrange).

Simplifying by Common Factor

The algebraic method of reducing a fractional expression to its simplest form by canceling out identical non-zero factors shared between the numerator $A(x)$ and the denominator $B(x)$.

Difference of Two Squares Identity

The factoring formula $a^2 - b^2 = (a - b)(a + b)$, utilized to factorize expressions such as $(3x - 2)^2 - (2x + 5)^2$ and simplify calculations like $50001^2 - 49999^2$.