How do you simplify rational expressions?
Factor the numerator and denominator, then cancel out any common factors.
How do you add or subtract rational expressions?
Find the LCD, rewrite each fraction with the LCD, then add or subtract the numerators.
How do you multiply rational expressions?
Multiply the numerators and denominators straight across, then simplify.
How do you divide rational expressions?
Multiply by the reciprocal of the second expression, then simplify.
How do you simplify complex fractions?
Multiply the numerator and denominator by the LCD of all internal fractions.
Explain how to factor using the difference of squares.
Identify two terms that are perfect squares separated by a minus sign, then apply the formula $a^2 - b^2 = (a+b)(a-b)$.
Explain how to factor a four-term polynomial by grouping.
Group the first two terms and the last two terms, factor out the GCF from each group, and then factor out the common binomial factor.
What is the first step when simplifying any rational expression?
Factor the numerator and denominator completely.
How do you determine restrictions on the variable in a rational expression?
Set the denominator equal to zero and solve for the variable. The solutions are the values that must be excluded.
When adding fractions, what must be the same?
The denominators.
What is a rational expression?
A fraction where the numerator and denominator are polynomials.
What is the Greatest Common Factor (GCF)?
The largest factor that divides two or more numbers or algebraic terms.
State the difference of squares formula.
$a^2 - b^2 = (a+b)(a-b)$
State the sum of cubes formula.
$a^3 + b^3 = (a+b)(a^2-ab+b^2)$
State the difference of cubes formula.
$a^3 - b^3 = (a-b)(a^2+ab+b^2)$
What is the Least Common Denominator (LCD)?
The smallest multiple that is common to two or more denominators.
What is a complex fraction?
A fraction containing one or more fractions in its numerator, denominator, or both.
What does it mean to simplify a rational expression?
To reduce the expression to its simplest form by factoring and canceling common factors.
When is long division used with rational expressions?
When the degree of the numerator is greater than or equal to the degree of the denominator.
What is the reciprocal of a fraction $\frac{a}{b}$?
$\frac{b}{a}$
