1.5, 1.6 Rational Equations & Inequalities

Solving Rational Equations

Multiply each side by the LCD of the rational equation to get rid of the fractions

solve normally using the previously stated techniques

extraneous solution set

is a set of solutions that are not answers to the original equation

empty set

a set containing no elements

is used to indicate that a solution doesn't exist for some particular equation

solving equations with radicals

1. Isolate the radical

2. Raise each side to the power that cancels the radical

3. solve for x using any method

solving equations with two radicals

isolate one radical at a time and then follow as usual

intersection

"and"

union

"or"

interval notation

A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval.

inequality notation

Uses inequality symbols to represent the boundaries of the domain or the range of a set of values.

graph notation