Definition of rational algebraic expression

Answer 1

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/2

Since the denominator is 2, which is a constant, the expression is defined for all real number values of x.

2) 2/x

Since the denominator x is a variable, the expression is undefined when x = 0

3) 2/(x - 1)

x - 1 ≠ 0

x ≠ 1

The 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.

Answer 2

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