# What constitutes a rational expression? How would you explain this concept to someone unfamiliar with it?

Posted on

A rational expression is of the form `(P(x))/(Q(x))` where P(x) and Q(x) are polynomials and Q(x) is not identically zero. (Note that x need not be a variable.) ((Also note that Q(x) can be zero for some values of x; just not every value of x.))

Rational expressions behave much as fractions do -- you add them by finding a common denominator, you multiply by multiplying numerator by numerator and denominator by denominator. And like fractions you can srite them as a "mixed number"; in this case as a polynomial plus a rational expression by using long division much like you would write a fraction as a mixed number by employing division.

Posted on

A rational expression is of the form where P(x) and Q(x) are polynomials in x and Q(x) is  identically not equal to zero.

`R(x)={(P(x))/(Q(x)): P(x), Q(x) are polynomial, Q(x)! -=0 }`

Please note here that " `Q(x)!-=0` " mean Q(x) is ndentically not equals to zero.

Since Q(x) is polynomial ,so it may have zeros / zero , it may concern when we talk about domain and range of  Rational expresion R(x).

Rational expressions behave much same  as rational numbers .    We  add them by finding a common denominator (LCD) ,  multiply by multiplying numerator by numerator and denominator by denominator. We can divide  like, in  rational numbers, and write them as a "mixed number". Similarly here also we can divide , by using long division and write them as polynomial plus rational expression i.e  " mixed expression " .

R(x) ,rational expressions are function.

Sources: