When a function is represented by ratio of two polynomials then this function is called as rational expression. In other words a Rational Expression is a fraction which is comprised of numerator and denominator where numerator and denominator are in polynomial form. Let’s try to understand the concept of rational function. Let’s consider a function f (y) which is represented as follows:
f (y) = A (y) / B (y).
Where A (y) and B (y) are two polynomials and function f (y) is called as Rational Expressions. A function that cannot be written in this form is not a rational function as f (y) = sin y is not a rational function. Here polynomial in denominator cannot be zero that is B (y) ≠ 0. Each of the polynomial is a rational function with B (y) = 1. (5 / x – 2), (x^{2} – 2) / (x^{2} + 3) are representing the rational expressions.
To solve a rational expression, rational expression must be reduced to its lowest term. To solve a rational function we need to make denominator same.
Let’s take an example to understand the concept of simplifying rational expressions and solving rational expressions.
(A^{2} – 2A – 8) / (A^{2} – 9A + 20),
This can be solved by factoring numerator and denominator which will be:
(A^{2} – 2A – 8) = (A – 4) (A + 2) and
(A^{2} – 9A + 20) = (A – 5) (A – 4),
Then solution will be:
(A^{2} – 2A – 8) / (A^{2} – 9A + 20) = (A – 4) (A + 2) / (A – 5) (A – 4),
Term (A – 4) in numerator and the denominator cancels each other and solution will be
(A^{2} – 2A – 8) / (A^{2} – 9A + 20) = (A + 2) / (A – 5).
An equation having rational expressions means it has a P/Q form with Numerators and Denominators as Constants or Variables. An example of it can be: (8/x) + (3/4) = 1. Let us take an example to show Solving Equations with Rational Expressions:
Our rational equation: (2 / x) + (3 / 4) = 1. One necessary assumption to be made is: x ≠ 0, reason be...Read More
Rational function is a function which is represented by ratio of two polynomials and a rational expression is that fraction which contains numerator and denominator. There are various rational expressions applications such as word form representation, almost all mathematical calculations numerical, analysis for interpolation and approximation of functions. Numerator and denom...Read More