Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
1. Simplifying Rational Expressions
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Exercise 4 Page 667

Practice makes perfect
a Recall that a rational expression is a fraction whose numerator and denominator are polynomials.
We will review two important definitions before making our determinations. With this information in mind, let's consider the given expression.
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 No
Denominator Yes

The numerator of the expression is a sum of and Since 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.
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.
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 Yes
Denominator 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 and a real number so it is also a polynomial. Therefore, the given expression is a rational expression.