Which of the following are rational expressions? (a) (3 x)/(x^2-1) (b) (√(x+1))/(2 x+3)

step 1 So we're asked to find which out of these three are rational expressions. So rational expression

Which of the following are rational expressions? (a) (3...

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Key Concepts

Polynomials

Polynomials are algebraic expressions that involve sums, differences, or products of variables raised to non-negative integer powers with constant coefficients. They form the building blocks for rational expressions when used as both numerators and denominators.

Radical Expressions

Radical expressions involve roots, such as square roots, where the variable is under a radical sign. These expressions are typically not considered polynomials, and if a radical appears in either the numerator or denominator, the overall expression does not meet the criteria for a rational expression.

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. The expression qualifies as rational if it meets this requirement and the denominator is not zero, ensuring that the expression is defined at most points in its domain.

Domain Considerations

When working with rational expressions, it is essential to account for values that make the denominator zero, as these values are excluded from the domain. Similarly, if there are radicals, one must also consider restrictions on the domain imposed by the need for non-negative radicands in even roots.

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