Math 3 Unit 4 Lesson 3 Review

Front

What makes a rational expression undefined?

Back

A rational expression is undefined when its denominator equals zero. For example, in the expression \( \frac{1}{x-3} \), it is undefined when \( x = 3 \).

Front

What are domain restrictions in rational expressions?

Back

Domain restrictions are values that make the denominator of a rational expression equal to zero, thus making the expression undefined. For example, for \( \frac{1}{x-4} \), the restriction is \( x \neq 4 \).

Front

Simplify the expression: \( \frac{4}{12ab} + \frac{3a}{4b^2} \)

Back

The simplified form is \( \frac{4b + 9a^2}{12ab^2} \).

Front

Simplify the expression: \( 3 + \frac{6x}{x+1} \)

Back

The simplified form is \( \frac{9x + 3}{x + 1} \).

Front

What is the first step in simplifying a rational expression?

Back

The first step is to find a common denominator for all terms in the expression.

Front

How do you find the least common denominator (LCD) of two fractions?

Back

The least common denominator is found by determining the least common multiple (LCM) of the denominators of the fractions.

Front

What is the process of combining fractions?

Back

To combine fractions, convert them to have a common denominator, then add or subtract the numerators while keeping the common denominator.

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials.

Front

What is the significance of factoring in simplifying rational expressions?

Back

Factoring allows you to cancel common factors in the numerator and denominator, simplifying the expression.

Front

What is the result of subtracting two fractions with different denominators?

Back

To subtract two fractions with different denominators, find a common denominator, convert each fraction, and then subtract the numerators.