Simplify Rational Algebraic Expressions In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section,

Simplify Rational Algebraic Expressions

In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section, we will use the factoring methods to simplify rational expressions.


In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section, we will use the factoring methods to simplify rational expressions.

A rational expression is simply a fraction that has polynomial expressions contained in the numerator and denominator…and the denominator can not equal zero



I started you off with a simple one to get us started…


STEP #1 : FACTOR all expressions completely





STEP # 2 : Look for COMMON FACTORS to “cancel”





WARNING !!!


WARNING !!!

You CAN NOT start by dividing individual terms to simplify…


WARNING !!!


WARNING !!!


WARNING !!!


WARNING !!!


WARNING !!!


WARNING !!!

So as a general rule, if you see + / - signs separating terms, you must factor to get common terms to simplify. You can only cancel multiplied terms.






Factors of 4 that add/subtract = - 3 are - 4 and + 1



Factors of 4 that add/subtract = - 3 are - 4 and + 1Factors of 4 that add/subtract = - 5 are - 4 and - 1



Factors of 4 that add/subtract = - 3 are - 4 and + 1Factors of 4 that add/subtract = - 5 are - 4 and - 1

STEP # 2 : Look for COMMON FACTORS to “cancel”

















STEP # 2 : Look for COMMON TERMS to “cancel”

Documents

Simplify Rational Algebraic Expressions In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section,