Rational Expression
A rational expression is a fraction where both the numerator and the denominator are polynomials
A rational expression is a fraction where both the numerator and the denominator are polynomials. In other words, it is an expression that involves a ratio of polynomial expressions.
The general form of a rational expression is:
P(x)
——
Q(x)
where P(x) and Q(x) are polynomials, and Q(x) is not equal to zero.
Rational expressions can be simplified by reducing them to their simplest form, just like fractions. This involves factoring the numerator and denominator and canceling out common factors. Simplifying a rational expression helps in evaluating its behavior, finding its domain and range, and solving equations and inequalities involving it.
For example, consider the rational expression (3x^2 + 6x) / (2x^2 – 4x). To simplify this expression, we can first factor the numerator and denominator:
3x(x + 2)
———-
2x(x – 2)
Then, we can cancel out the common factor of 3x in the numerator and denominator:
(x + 2)
——–
(x – 2)
The simplified form of the given rational expression is (x + 2) / (x – 2). This expression represents a ratio of polynomials and can be used to perform various mathematical operations or analyze its properties.
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