A **rational expression** is a fraction in which the
numerator or denominator is a

variable expression (such as a polynomial).

A rational expression is in SIMPLEST form when the numerator and denominator

have no comman factors other than 1.

**Reducing to simplest form** – factor the numerator and denominator, then
cancel out

any common factors in the numerator and denominator (not common factors that are

both in the numerator or both in the denominator, e.g. side by side).

**Multiplying Rational Expressions** – factor the numerators and denominators
then

cancel out common factors as above, then multiply the numerators and multiply
the

denominators.

**Dividing Rational Expressions** – change to a multiplication problem by
changing

the DIVISOR into it’s RECIPROCAL.

**Adding and Subtraction Rational Expressions **–

Step 1:Factor the denominators, then find the LCM. The LCM of two polynomials is

the simplest polynomial that contains the factors of each polynomial. To find
the

LCM of two or more polynomials, first factor each polynomial completely. The

LCM is the product of each factor the great number of times it occurs in any one

factorization.

Step 2: Change each rational expression so that the new denominator will be the

LCM. You will multiply tne numerator and denominator of each expression by

whatever it takes to get the LCM as the new denominator.

Step 3: Add the two new fractions by adding the numerators and keeping the

denominator (the LCM) the same.

Step 4: Now factor the resulting expression and cancel out any common factors in
the

numerator and denominator.

**
Simplify Complex Fractions** – Complex fractions are just rational expressions
with

fractions within fractions. To simplify, find the LCM of all the denominators of

every fraction in the expression, then multiply the main numerator and denominator

by that LCM. Then simplify as usual.

LCM of all denominators in the equation. Then solve as usual.

If the equation is one fraction set equal to another, this is called a PROPORTION.

Solve by CROSS-MULTIPLYING, then isolating the variable.

APPLICATIONS OF RATIONAL EXPRESSIONS

**Similar Triangles**

Triangles are similar if at least 2 corresponding angles are the same

in each triangle.

**WORK
Rate of Work * Time Worked= Part of Tasked Completed**

If someone can do a job in 60min, their rate of work is 1/60min.

If someone else can do the same job in 40minutes, their rate of work

is 1/40min.

The TIME to get the same job done TOGETHER can be found by

Adding their parts together to make 1 whole job.