With this information in mind, let's consider the given expression.
sqrt(x)+2/x^2+4
To decide whether or not the above expression is a rational expression, we have to check if its numerator and denominator are polynomials.
Expression
Is It a Polynomial?
Numerator
sqrt(x)+2
No
Denominator
x^2+4
Yes
The numerator of the expression is a sum of sqrt(x) and 2. Since sqrt(x) is not a monomial, the numerator is not a polynomial. Therefore, the given expression is not a rational expression.
b Recall that a rational expression is a fraction whose numerator and denominator are polynomials.
Rational Expression:polynomial/polynomial
We will review two important definitions before making our determinations.
Polynomial: a monomial or a sum of monomials.
Monomial: a real number, a variable, or a product of a real number and one or more variables with whole number exponents.
With this information in mind, let's consider the given expression.
y/y-1
To decide whether or not the above expression is a rational expression, we have to check if its numerator and denominator are polynomials.
Expression
Is It a Polynomial?
Numerator
y
Yes
Denominator
y-1
Yes
The numerator of the expression is a monomial, so it is a polynomial. The denominator of the expression is a sum of a monomial y and a real number - 1, so it is also a polynomial. Therefore, the given expression is a rational expression.
