expression is undefined when that is, ( p = − , p = − . The excluded values are - and - . (iii) x Here, x ³ for all x . Therefore, x ≥ = .
Hence, x + ≠ for any x . Therefore, there can be no real excluded values for the given rational expression x + . Thinking Corner . Are x - and tan rational expressions?
. The number of excluded values of x is . Exercise . .
Reduce each of the following rational expressions to its lowest form. (i) x (ii) x (iii) (iv) . Find the excluded values, if any of the following expressions. (i) y (ii) t t t (iii) x (iv) .
. Operations of Rational Expressions We have studied the concepts of addition, subtraction, multiplication and division of rational numbers in previous classes. Now, let us generalize the above for rational expressions. Multiplication of Rational Expressions If p x q x ( ) and r x s x ( ) are two rational expressions where q x s x , ( ) ¹ ¹ , their product is p x q x r x s x ´ p x r x q x s x In other words, the product of two rational expression is the product of their numerators divided by the product of their denominators and the resulting expression is then reduced to its lowest form.
Division of Rational Expressions If p x q x ( ) and r x s x ( ) are two rational expressions, where q x s x ( ), ( ) ¹ then, p x q x r x s x √ p x q x s x r x ( ) = p x s x q x r x Thus division of one rational expression by other is