Rational Algebraic Expression

Qtr1_Module2_week2

Illustrating Rational Algebraic

Expressions

Illustration of A Rational Algebraic Expression

A rational algebraic expression is an expression that can be written in the form 𝑃 𝑄 where 𝑷 and 𝑸 are polynomials and 𝑸 must not be equal to 0 (Q ≠ 0).

In other words, a rational algebraic expression is an expression whose numerator and denominator are polynomials. From the previous activity, expressions formed in items 1,2 and 3 are rational algebraic expressions because the numerator and the denominator are both polynomials. On the other hand, expressions formed in items 4, 5, and 6 are not rational algebraic expressions because the numerator and denominator of the expressions are not polynomials. 

Illustration of A Rational Algebraic Expression

How will you know that the expression is a rational algebraic expression? For you to recognize rational algebraic expressions, examine the following examples.

Presentation 1: Check these expressions.

All of the expressions here are rational algebraic expressions since these contain polynomial expressions in both numerator and denominator, respectively.

Illustration of A Rational Algebraic Expression

Presentation 2: Check these expressions: 

All of the expressions here are not rational algebraic expressions since the expressions contain irrational numbers (√𝑥 and √𝑦) and variables having negative exponents (𝑥^-2 and 𝑧^-2 ), which are not polynomials.

Illustration of A Rational Algebraic Expression

Here’s a useful checklist in identifying whether the expression is a rational algebraic expression:

 The expression must be in fraction form.

 The expression must have in its numerator and denominator a constant, a variable, or a combination of both, that are polynomial expressions.

 The expression must not have a negative exponent, a radical sign or a fraction exponent in the variable/s in both numerator and denominator.

Illustration of A Rational Algebraic Expression

Recall that the rational algebraic expression is a fraction containing polynomials in both numerator and denominator, provided that the denominator must not be equal to zero. The denominator cannot be zero because a division of 0 is undefined or meaningless. In rational algebraic expressions, you need to pay attention to what values of the variables that will make the denominator equal to 0. These values are called excluded values. How are you going to determine the excluded value/s in a rational algebraic expression?

Steps in Determining the Excluded Values:

(Study Tip: Just pay attention to the denominator of the expression to determine the excluded values.) Step

1: Let the expression in the denominator be equal to 0. Step

2: Solve the equation to determine the value/s of the variable. 

Here are the illustrative examples that will help you understand it better