How to Simplify Rational Expressions

How to Simplify Rational Expressions Rational expression is a ratio of two polynomial expressions. For example: - 3 x^2 / 6x (x^2 + 4 x + 4) / (2 x + 4) (x^2 9) / (x^3 -9 x^2 +27 x 9) and so on. How to simplify rational expressions: - Example 1: - Simplify 3 x^2 / 6x Solution: - Cancel out the common factor of the numerator and denominator. Common Factor of 3x^2 and 6x is 3x. Hence we can write 3 x^2 / 6x = 3x *x / 3x * 2 = x /2 Answer: - Therefore, 3 x^2 / 6x = x / 2. Example 2: - Simplify (X^2 + 4 x + 4) / (2 x + 4) Solution: - i) Factor the numerator. Therefore (X^2 + 4 x + 4) = x^2 + 2 * x^2 * 2 + 2^2 = (x + 2)^2 [Since (a + b)^2 = a^2 + 2ab + b^2] ii) Take the common factor of the denominator Therefore (2 x + 4) = 2 (x + 2). iii) Cancel out the common term of the numerator and denominator, therefore we can write, (X^2 + 4 x + 4) / (2 x + 4) = (x + 2)^2 / 2 (x + 2) = (x + 2) / 2 Example 3: - Simplify (x^2 9) / (x^3 -9 x^2 +27 x 9) Solution: - Similarly (x^2 9) / (x^3 -9 x^2 +27 x 9) = (x+3) (x - 3)/(x - 3) ^3 = (x+3)/(x-3) ^2