4
@12 Simplifying
%3
^1
Algebraic fractions can be reduced only 
if a factor of the numerator also 
occurs as a factor of the denominator.
^2
When reducing a fraction with two 
monomials, first reduce the numerical 
coefficient factors.
^3
Next, reduce the variable factors. If 
similar variables have exponents, 
subtract the smaller exponent from the 
larger.  Put the result where the 
larger exponent was and simplify.
~
%3
^1
The quotient of two polynomials is one 
type of algebraic fraction.  Factor 
before dividing.
^2
First, factor the numerator, then the 
denominator.
^3
Cancel any factor which appears in both 
the numerator and the denominator and 
simplify. 
~
@22 Multiplying and Dividing
%3
^1
When an algebraic fraction contains 
polynomials, factor before dividing 
or multiplying.
^2
First factor the polynomials.
Write as a single fraction.
^3
Cancel any factor which appears in both 
the numerator and denominator.  
Simplify.
~
%4
^1
Dividing by an algebraic fraction is 
the same as multiplying by the 
reciprocal of that fraction.  
^2
Rewrite the problem as multiplication.
^3
First factor the polynomials.
Write as a single fraction.
^4
Cancel any factor which appears in both 
the numerator and the denominator.  
Simplify.
~
@32 Adding and Subtracting
%3
^1
Fractions must have common denominators 
in order to be added or subtracted.
^2
Add or subtract the numerators.
^3
Reduce the result whenever possible.
~
%7
^1
Fractions must have common denominators 
in order to be added or subtracted.
^2
First, factor each binomial denominator.
^3
Determine the lowest common denominator 
(LCD).  Write the LCD as a product 
containing each different factor found 
in the denominators.
^4
Multiply the numerator and denominator 
of each fraction by the factor needed 
to create the LCD.
^5
Simplify.
^6
Combine the numerators, now that they 
have common denominators.
^7
Reduce the result if possible, and 
simplify.
~
@42 Solving Fractional Equations
%5
^1
One method of solving a fractional 
equation is to eliminate the 
denominators.
^2
First, find the LCD of the fractions.
^3
Multiply each term of the equation by 
the LCD.
^4
Simplify and eliminate all 
denominators.
^5
Solve the resulting equation.
~
%5
^1
A fractional equation can be solved 
most easily by first using the 
Multiplication Property to eliminate 
the denominators.
^2
First, find the LCD of the fractions.
^3
Multiply each term of the equation by 
the LCD.
^4
Simplify and eliminate all 
denominators.
^5
Solve the resulting equation using the 
steps you have learned.
~                                        

