Adding And Subtracting Rational Expressions

Adding And Subtracting Rational Expressions Rational expression is a fraction of two polynomials When polynomials in the denominator 0. For example: - (x^1 + 2)/ (x^2 + 1) is a rational expression where x^2 + 1 0. Other examples of rational expressions like (x + 1) / (x + 2) (3x^2 + 2) / (x + 5) (9x^3 + 6x^2 + 8x + 5) / (7x^2 + 5x + 9) 3/ x 5 / (x + 1) Few examples those are not a rational expressions: - [5 + x^(3/2)] / (x + 9): - It is not a rational expression because 5 + x^ (3/2) is not a polynomial. Polynomial defines that the power should be non- negative intger but 3/ 2 is not an integer. [1 + x ^ (-1)] / x: - -1 is a negative number so numerator is not a polynomial. Hence it is not a rational expression. 2x / [x ^ (2) + 5]: - 2 is not integer so it is not a rational expression. Examples of Adding and subtracting rational expressions: - Add the following rational expressions: - (3x + 2) / x^2, (x^2 + 2) / x^3. Solution: - (3x + 2) / x^2 + (x^2 + 2) / x^3 =[ x (3x + 2) + (x^2 + 2)] / x^3 = (3x^2 + 2x + x^2 + 2) / x^3 = (4x^2 +2x + 2) / x^3 = 2(2x^2 + x + 1) / x^3 Simplify: - (x+1)/(x-1) (x-1)/(x+1) Solution: - [(x+1)^2-(x-1)^2]/[(x+1)(x-1)] =[(x^2+2x+1)-(x^2-2x+1)]/(x^2-1^2) =(x^2+2x+1-x^2+2x-1)/(x^2-1) =4x/(x^2-1)