Definition of rational algebraic expression? - Answers

A rational number is any number that can be written in the form a/b, where a and b are integers and b ≠ 0. it is necessary to exclude 0 because the fraction represents a ÷ b, and division by zero is undefined.A rational expression is an expression that can be written in the form P/Q where P and Q are polynomials and the value of Q is not zero.Some examples of rational expressions:-5/3; (x^2 + 1)/2; 7/(y -1); (ab)/c; [(a^2)(b]/c^2; (z^2 + 3z + 2)/ (z + 1) ect.Like a rational number, a rational expression represents a division, and so the denominator cannot be 0. A rational expression is undefined for any value of the variable that makes the denominator equal to 0. So we say that the domain for a rational expression is all real numbers except those that make the denominator equal to 0.Examples:1) x/2Since the denominator is 2, which is a constant, the expression is defined for all real number values of x.2) 2/xSince the denominator x is a variable, the expression is undefined when x = 03) 2/(x - 1)x - 1 ≠ 0x ≠ 1The domain is {x| x ≠ 1}. Or you can say:The expression is undefined when x = 1.4) 2/(x^2 + 1)Since the denominator never will equal to 0, the domain is all real number values of x.