DIFFERENCE BETWEEN RATIONAL NUMBER AND RATIONAL EXPRESSION:

 First we discuss about definitions of rational number , rational expression and terms involved in definition.

Definition Of Rational Number:

A number which is written in form of  p/q ,where q does not equal to 0 and p,q must be integers.

(integers I={---,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,---})

Examples:  -7/5,2/3,0=0/1,2=2/1,5/2 etc.

Explaination: Here we take one of above example like -7/5 .

Comparing -7/5 by p/q,we find p=-7 and q=5(which is not equal to 0) therefore by definition -7/5 is a rational number.

Definition Of Rational Expression:

An expression which is in form of p(x)/q(x),where q(x) does not equal to zero(0) polynomials and p(x),q(x) must be polynomials in x.

(polynomials like x+4,x^2+9,x^4+5 etc are polynomials of degrees 1,2,4 respectively).

Examples: (x+5)/(x+4), comparing this expression

by p(x)/q(x),we find p(x)=(x+5) and q(x)=(x+4)(which is not equal to 0 polynomial) therefore by definition (x+5)/(x+4) is a rational expression.

(expression are made up of variables like x,y(generally taken x) and constants)

DIFFERENCE BETWEEN RATIONAL NUMBER AND RATIONAL EXPRESSION:

Rational number is a number which is explained in definition but rational expression is not a number ,it is an expression  which is explained in definition.

Now we differentiate between two by taking  examples.

We take 5/7,it is no doubt that it is a rational number by above definition of rational number.

Now we check whether it is rational expression or not.Comparing 5/7 by p(x)/q(x) ,we find p(x)=5=5*x^0(which is polynamial of zero degree) and q(x)=7(which is also a polynomial of zero degree) but q(x) does not equal to 0 therefore by definition it is a rational expression.

By this example we see that 5/7 is rational number and rational expression also.

CONCLUSION:  Each and every rational number is rational expression but its vice-versa is not true.