Advanced Algebra - Rational Expressions

Front

What makes a rational expression undefined?

Back

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

Tags

CCSS.HSA.APR.D.7

Front

How do you find the values that make a rational expression undefined?

Back

To find the values that make a rational expression undefined, set the denominator equal to zero and solve for the variable. For example, for \( \frac{1}{x^2 - 4} \), set \( x^2 - 4 = 0 \) to find \( x = 2 \) and \( x = -2 \).

Tags

CCSS.HSA.APR.D.7

Front

What is the Greatest Common Factor (GCF)?

Back

The Greatest Common Factor (GCF) is the largest factor that divides two or more numbers. For example, the GCF of 12 and 16 is 4.

Front

How do you multiply rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together. For example, \( \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \).

Tags

CCSS.HSA.APR.D.7

Front

What is the process for dividing rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the second expression. For example, \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \).

Tags

CCSS.HSA.APR.D.6

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by canceling common factors in the numerator and denominator.

Tags

CCSS.HSA.APR.D.6

Front

What is a rational expression?

Back

A rational expression is a fraction where the numerator and the denominator are polynomials. For example, \( \frac{x^2 + 2x + 1}{x - 1} \) is a rational expression.

Tags

CCSS.HSA.APR.D.7

Front

How do you add rational expressions with different denominators?

Back

To add rational expressions with different denominators, find a common denominator, convert each expression, and then add the numerators. For example, \( \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \).

Tags

CCSS.HSA.APR.D.7

Front

What is the difference between a proper and improper rational expression?

Back

A proper rational expression has a numerator with a lower degree than the denominator, while an improper rational expression has a numerator with a degree equal to or higher than the denominator.

Tags

CCSS.HSA.APR.D.6

Front

How do you factor a polynomial?

Back

To factor a polynomial, look for common factors, use grouping, or apply special factoring formulas like the difference of squares. For example, \( x^2 - 9 = (x - 3)(x + 3) \).

Tags

CCSS.HSA.APR.C.4