Unit 5 Radical and Rational Expressions

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x or ∛(x+1) are radical expressions.

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are both polynomials. For example, (2x + 3)/(x^2 - 1) is a rational expression.

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator, then cancel any common factors.

Front

What is the process for adding rational expressions?

Back

To add rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What is the difference between a radical and a rational expression?

Back

A radical expression involves roots, while a rational expression is a ratio of two polynomials.

Front

What is the domain of a rational expression?

Back

The domain of a rational expression includes all real numbers except those that make the denominator zero.

Front

What is the first step in simplifying the expression 7/(m-3)?

Back

The first step is to check if the expression can be factored further, but in this case, it is already in its simplest form.

Front

How do you solve for a variable in a rational equation?

Back

To solve for a variable in a rational equation, first eliminate the fractions by multiplying both sides by the least common denominator (LCD), then solve the resulting equation.

Front

What is the significance of the least common denominator (LCD) in adding rational expressions?

Back

The least common denominator (LCD) is used to ensure that all fractions have the same denominator, allowing for proper addition of the numerators.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction by multiplying the numerator and denominator by a suitable radical.