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In this page we are going to discuss about simplifying rational expressions concept . A rational expression is an expression of the form P(x) / Q(x) over the set of real numbers and Q(x) ? 0 where P(x) and Q(x) are two polynomials. It is the quotient of two polynomials. For example: 3 / x2 , (x4 + x3 + x + 1) / (x + 6) , 5 / (x + 8) , (x – 2) / (x + 2) , 28y-3 are all rational algebraic expressions. How to simplify rational expressions Let's see some examples on how to simplify rational expressions - Rational algebraic expressions P(x) / Q(x) can be reduced to its lowest term by dividing both numerator P(x) and denominator Q(x) by the G.C.D. of P(x) and Q(x). Example 1: Simplify the rational algebraic expression (5x + 20) / (8x + 32) Solution: (5x + 20) / (8x + 32) = 5(x + 4) / 8(x + 4) Cancel (x + 4) term from both numerator and denominator, (5x + 20) / (8x + 32) = 5 / 8 Example 2: Simplify (5x + 20) / (6x + 24) Solution: (5x + 20) / (6x + 24) = 5(x + 4) / 6(x + 4) Cancel (x + 4) term from both numerator and denominator, (5x + 20) / (6x + 24) = 5 / 6
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