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Please provide an example of a rational expression.

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telesco79 | Student, College Freshman | Honors

Posted December 15, 2012 at 4:08 PM via web

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Please provide an example of a rational expression.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted December 15, 2012 at 4:40 PM (Answer #1)

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You should know that a rational expression has as numerator and denominator polynomials such that:

`(a_n*x^n + a_(n-1)*x^(n-1) + ...... + a_1*x + a_0)/(b_m*x^m + b_(m-1)*x^(m-1) + .... + b_1*x + b_0)`

Notice that the numerator and denominator are polynomials `P(x) = a_n*x^n + a_(n-1)*x^(n-1) + ...... + a_1*x + a_0`  and `Q(x) = b_m*x^m + b_(m-1)*x^(m-1) + .... + b_1*x + b_0.`

You should know that a fraction is not defined if the denominator is zero, hence, there exists the rational expression `(P(x))/(Q(x))`  if polynomial `Q(x) != 0` .

The rational expressions are classified as proper and improper, such that:

-degree of polynomial `P(x) <`  degree of polynomial `Q(x), ` hence, the fraction is called proper fraction

-degree of polynomial `P(x)>`  degree of polynomial `Q(x), ` hence, the fraction is called improper fraction, and you need to simplify the fraction to its lowest terms.

Hence, you need to remember that a rational expression has as numerator and denominator two polynomials, `(P(x))/(Q(x)).`

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