ElementaryAlgebra2e-WEB_3zxfu3Z-181

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Solution
Write as to have 2 rational expressions.
Do the rational expressions have a common denominator? No.
Find the LCD of and LCD =
Rewrite as an equivalent rational expression with the LCD.
Simplify.
Subtract the rational expressions.
Simplify.
Factor to check for common factors.
There are no common factors; the rational expression is simplified.
TRY IT 8.95 Subtract:
TRY IT 8.96 Subtract:
HOW TO
Add or subtract rational expressions.
Step 1. Determine if the expressions have a common denominator.
Yes – go to step 2.
No – Rewrite each rational expression with the LCD.
Find the LCD.
Rewrite each rational expression as an equivalent rational expression with the LCD.
Step 2. Add or subtract the rational expressions.
Step 3. Simplify, if possible.
We follow the same steps as before to find the LCD when we have more than two rational expressions. In the next
example we will start by factoring all three denominators to find their LCD.
EXAMPLE 8.49
Simplify:
8.4 • Add and Subtract Rational Expressions with Unlike Denominators 891
Solution
Do the rational expressions have a common denominator? No.
Find the LCD.
Rewrite each rational expression as an equivalent rational expression with the
LCD.
Write as one rational expression.
Simplify.
Factor the numerator, and remove common factors.
Simplify.
TRY IT 8.97 Simplify:
TRY IT 8.98 Simplify:
SECTION 8.4 EXERCISES
Practice Makes Perfect
In the following exercises, find the LCD.
169. 170. 171.
172. 173. 174.
175. 176.
In the following exercises, write as equivalent rational expressions with the given LCD.
177.
LCD
178.
LCD
179.
LCD
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180.
LCD
181.
LCD
182.
LCD
183.
LCD
184.
LCD
In the following exercises, add.
185. 186. 187.
188. 189. 190.
191. 192. 193.
194. 195. 196.
197. 198. 199.
200. 201. 202.
203. 204. 205.
206. 207. 208.
In the following exercises, subtract.
209. 210. 211.
212. 213. 214.
215. 216. 217.
218. 219. 220.
221. 222. 223.
224. 225. 226.
227. 228.
In the following exercises, add and subtract.
229. 230. 231.
232.
In the following exercises, simplify.
233. 234. 235.
236. 237. 238.
239. 240. 241.
242. 243. 244.
8.4 • Add and Subtract Rational Expressions with Unlike Denominators 893
245. 246. 247.
248. 249. 250.
Everyday Math
ⓐ Find the fraction of the decorating job that
Victoria and her sister, working together, would
complete in one hour by adding the rational
expressions
ⓑ Evaluate your answer to part (a) when
251. Decorating cupcakes Victoria can decorate an
order of cupcakes for a wedding in hours, so in
1 hour she can decorate of the cupcakes. It
would take her sister 3 hours longer to decorate
the same order of cupcakes, so in 1 hour she can
decorate of the cupcakes. ⓐ Find an expression for the number of hours
it would take Trina to kayak 5 miles up the river
and then return by adding
ⓑ Evaluate your answer to part (a) when
to find the number of hours it would take Trina if
the speed of the river current is 1 mile per hour.
252. Kayaking When Trina kayaks upriver, it takes her
hours to go 5 miles, where is the speed of
the river current. It takes her hours to kayak
5 miles down the river.
Writing Exercises
ⓐ Choose numerical values for x and y and
evaluate
ⓑ Evaluate for the same values of x and y
you used in part (a).
ⓒ Explain why Felipe is wrong.
ⓓ Find the correct expression for
253. Felipe thinks is 254. Simplify the expression and
explain all your steps.
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ On a scale of 1-10, how would you rate your mastery of this section in light of your responses on the checklist? How
can you improve this?
8.5 Simplify Complex Rational Expressions
Learning Objectives
By the end of this section, you will be able to:
Simplify a complex rational expression by writing it as division
Simplify a complex rational expression by using the LCD
BE PREPARED 8.17 Before you get started, take this readiness quiz.
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If you miss a problem, go back to the section listed and review the material.
Simplify:
If you missed this problem, review Example 1.72.
BE PREPARED 8.18 Simplify:
If you missed this problem, review Example 1.74.
Complex fractions are fractions in which the numerator or denominator contains a fraction. In Chapter 1 we simplified
complex fractions like these:
In this section we will simplify complex rational expressions, which are rational expressions with rational expressions in
the numerator or denominator.
Complex Rational Expression
A complex rational expression is a rational expression in which the numerator or denominator contains a rational
expression.
Here are a few complex rational expressions:
Remember, we always exclude values that would make any denominator zero.
We will use two methods to simplify complex rational expressions.
Simplify a Complex Rational Expression by Writing it as Division
We have already seen this complex rational expression earlier in this chapter.
We noted that fraction bars tell us to divide, so rewrote it as the division problem
Then we multiplied the first rational expression by the reciprocal of the second, just like we do when we divide two
fractions.
This is one method to simplify rational expressions. We write it as if we were dividing two fractions.
EXAMPLE 8.50
Simplify:
8.5 • Simplify Complex Rational Expressions 895
	Chapter 8 Rational Expressions and Equations
	8.5 Simplify Complex Rational Expressions