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Rational Expression
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Rational Expression
A rational expression is an algebraic expression of the form R/S, where R and S are simple expressions (usually polynomials), and the denominator S is not zero.

To write a rational expression in lowest terms, first find all common factors (constants, variables, or polynomials) of the numerator and the denominator. So, factor the numerator and the denominator. Then cross out all common factors.
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Example: Reduce the following rational expressions to its lowest terms.
(i) x2+10x+24/x2+5x-6      
(ii) x2+7x+12/x2+5x+6

Solution:

(i)Given: x2+10x+24/x2+5x-6   
Let p(x) = x2+10x+24 = (x+6)(x+4)
And q(x) = x2+5x-6 = (x+6)(x-1)
So, g.c.d.[p(x),q(x)]= x+6.

Therefore,
 x2+10x+24/x2+5x-6 
= (x+6)(x+4)/(x+6)(x-1)
= (x+4)/(x-1) .....[Cancelling the g.c.d.]

Hence, the given rational expression in lowest terms is (x+4)/(x-1).

(ii)Given: x2+7x+12/x2+5x+6
Let p(x) = x2+7x+12 = (x+3)(x+4)
And q(x) = x2+5x+6 = (x+3)(x+2)
So, g.c.d.[p(x),q(x)]= x+3.

Therefore,
x2+7x+12/x2+5x+6
= (x+3)(x+4)/(x+3)(x+2)
= (x+4)/(x+2).....[Cancelling the g.c.d.]

Hence, the given rational expression in lowest terms is (x+4)/(x+2).
 
   
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