Skill Builder 8.1 Rational Expressions and Their Simplification

Transcription

1 Skill Builder 1 Rational Epressions and Their Simplification Simplif each rational epression. State all numbers for which each ration epression is undefined. If the rational epression cannot be simplified state so a a a 9 a a t t 4 4t 1t 16 a 6a 9 a S-4

2 Skill Builder Multipling and Dividing Rational Epressions Rational epressions are multiplied and divided the same wa rational numbers are multiplied and divided. Fill in the blanks. To multipl rational epressions each numerator and denominator first! To divide rational epressions b the reciprocal of the. Factoring is a ver important skill to master. Review factoring if ou are having difficult multipling and dividing rational epressions. Multipl or divide. a a 1 a a 1 a 6a 0 a 7a 11a 6 7a 4a ( ) S-4

3 Skill Builder Adding and Subtracting Rational Epressions with the Same Denominator Add or subtract as indicated. Simplif if possible S-44

4 Skill Builder 4 Adding and Subtracting Rational Epressions To add or subtract rational epressions the must have a common denominator. Build a common denominator from the factors of each denominator. Watch signs especiall when subtracting. Rational Epressions 4 1 a b. 4 1 c. 0 4 d. 1 9 Factors of First Denominator Factors of Second Denominator Least Common Denominator Add or subtract a a a 8 9. a a a S-4

5 Skill Builder Comple Rational Epressions Simplif each comple rational epression b the method of our choice. Reduce if possible a ab 1 a b b 1 S-46

6 Skill Builder 6 Solving Rational Equations A rational equation is an equation involving one or more rational epressions. Factor denominators to find Least Common Denominator (LCD). Multipl each term or epression in the equation b the LCD to get rid of the fractions. Check solutions for restricted values. Solve each equation. Fill in the chart. Equation LCD Restricted Values Check a a a 6 a a a 9 a a 9 S-47

7 Skill Builder 7 Applications Using Rational Equations and Variation In still water a boat averages miles per hour. It takes the same amount of time to travel 6 miles downstream with the current as it takes to travel 4 miles upstream against the current. What is the rate of the water s current? The water s current is 4 miles per hour. A boat can travel 0 miles downstream with the current in the same time it takes to travel miles upstream against the current. What is the boat s average rate in still water?. Coleman can grade a set of test papers in 1 minutes. Stac can grade the same number of test papers in minutes. How long will it take them to grade the set of papers working together? There are two separate drains to the tank at the farm. When the larger drain is used alone it can empt the tank in hours. If the smaller of the two drains is used alone it will take 6 hours. How long will it take to empt the tank if both drains are used? If a si foot lamp post casts a 14 foot shadow how tall would a flag pole be if it casts a foot shadow? Triangle PQR is similar to triangle XYZ. PQ measures 4 inches QR measures 8 XY measures. Find the measure of YZ. If varies directl as and 70 when 10 find if 1 If varies directl as and 10 when 1 find if If varies indirectl as and 7 when 10 find if If varies indirectl as and 4 when 8 find if 1 S-48