SAT SUBJECT TEST MATH LEVEL 1

ALGEBRA

CHAPTER 5 Polynomials

ALGEBRAIC FRACTIONS

Although the coefficient of any term in a polynomial can be a fraction, such as  the variable itself cannot be in the denominator. Expressions such as  which do have variables in their denominators, are called algebraic fractions. You will have no trouble manipulating algebraic fractions if you treat them as regular fractions, using all the standard rules for adding, subtracting, multiplying, and dividing.

Whenever you have to simplify an algebraic fraction, factor the numerator and denominator, and divide out any common factors.

TIP 

All the rules for numerical fractions apply to algebraic fractions.

EXAMPLE 9: Simplify .

Note that  is an identity. For every real number (except –2 and –3, for which the original fraction is undefined), the expressions have the same value. For example, when x = 8:

Similarly, when x = 3, both expressions equal 0, and when x = –4, both expressions equal 7.