
rational expressions
Complex rational expressions contain fractions within
fractions. This is un
desirable. We now learn how to turn complex rational expressions into the
preferable rational expression.
When would we encounter such a situation?
If and consider
, Then
We will learn two ways of accomplishing our goal. You may choose the one
you prefer.
Property 0.1 Simplify a Complex Rational Expresion by Multiplying by
1. Find the LCD of all rational expressions within the complex rational
expression.
2. Multiply both the numerator and denominator of the complex rational
expression by this LCD.
3. Use the distributive property and multiply each term in the numera
tor and denominator by the LCD. Simplify each term. No fractional
expressions should remain within the main fraction.
4. Factor and simplify.
Example 0.1
Property 0.2 Simplify a Complex Rational Expresion
by Dividing
1. Add or subtract to get a single expression in the numerator.
2. Add or subtract to get a single expression in the denominator.
3. Perform the division indicated by the main fraction bar. That is, invert
the denominator of the complex rational expression and multiply.
4. Simplify.
Example 0.2 Simplify a Complex Rational Expresion by Dividing
Example 0.3 Suppose
Find
Example 0.4 If three resistors with resistances R_{1},
R_{2}, and R_{1} are con
nected in parrallel, their combined resistance, R, is given by the formula
Simplify the complex rational expression on the right side
of the formula.
Then find R, to the nearest hundredth of an ohm, when R_{1} is 4
ohms, R_{2} is
8 ohms, and R_{3} is 12 ohms.
when R_{1} is 4 ohms, R_{2} is 8 ohms, and
R_{3} is 12 ohms
