A rational expression is defined as the ratio of two polynomials. For example , here is a polynomial of degree 2 and x + 1 is a polynomial of degree 1. For polynomials, the exponents of variables are always positive. is not a rational expression as is not a polynomial.
Example 1: Multiply the rational expressions and .
Multiplication of rational expressions:
Factoring the expressions. Factors of are (x + 3) (x – 3)
This is of the form - = (a + b) ( a – b). If we compare - with - then we get a = x and b = 3. Hence the factors are (x + 3) (x – 3)
Factors of are = (x + 1) (x + 1)
= (x – 3) (x + 1)
= + x – 3x – 3
= - 2x – 3
Hence the product of given rational expression is - 2x – 3.
Example 2: Dividing the rational expressions and.
Division of rational expressions: ÷
Writing the expressions into factors.
= (x + 5) (x + 2)
= (x + 7) (x – 2)
= (x+ 5) (x + 7)
Multiplication using FOIL method,
Multiplication of first terms x and x =
Multiplication of outer terms x and 7 = 7x
Multiplication of Inner terms 5 and x = 5x
Multiplication of Last terms 5 and 7 = 35
Adding all the terms = + 7x + 5x + 35 = + 12x + 35