chapter 8
8.1Multiplying and Dividing Rational Expression
To multiply rational expressions, first factor all numerators and denominators and cancel any factors you can. Then multiply what you have left. To divide, simply flip the divisor (the term you're dividing by) and then multiply. In math-speak, it's called multiplying by the reciprocal of the divisor.
example 
8.2 Adding & Subtracting Rational Expressions
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To add or subtract rational expressions
with unlike denominators,
first find the LCM of the denominator. ...
Write each expression using the LCD. ...
Add or subtract the numerators.
Simplify as needed.
example
8.3 The general form of a reciprocal function is r(x) = a / (x - h) + k. The graphs of reciprocal functions are made up of branches, which are the two main parts of the graph; and asymptotes, which are horizontal and vertical lines that the graph approaches but doesn't touch
example
8.4 Graphing Rational Functions
steps
See if there are any HOLES. ...
Find VERTICAL ASYMPTOTES by finding
where factors in the denominator equal zero. ...
See if the fraction is TOP HEAVY, BOTTOM
HEAVY, OR BALANCED for Non-Vertical
(Horizontal and Oblique/Slant) Asymptotes. ...
Find the x-intercepts where the numerator is equal to zero.
8.5 Variation Functions
8.6
Solving Rational Equations & Inequalities
Put the inequality in general form.
Set the numerator and denominator
equal to zero and solve. ...
Plot the critical values on a number line,
breaking the number line into intervals.
Take a test number from each interval
and plug it into the original inequality.
work done by:tala almousa 11c