PDF Notes, Examples, and practice (with solutions)
Word Problems that use Rational Expressions Example: Underground pipes can fill a swimming pool in 4 hours. A regular garden hose can fill the pool in 15 hours. If both are used at the same thne, how long will it take to fill the pool? Solving Rational Equalities/Equations Step 3: Check Answer! If time is 3.158 hours, the pipes will add
PDF 10 Math 51 Application problems with rational expressions
Application Problems with Rational Expressions The applications will involve situations with work rate, variations, water current and speed of wind. Work rate Work rate problems usually involve two people that are trying to help each other finish a single job. Fran can clean the garage in 3 hours, but it takes Angie 4 hours to do the same job.
PDF Sample Problems
Lecture Notes Rational Expressions page 4 Sample Problems Œ Solutions 1. Simplify each of the following. a) 2a 5 5 2a Solution: We need to notice that the numerator and denominator are opposites of each other. Indeed, the opposite of 2a 5 is 5 2a since 1(2a 5) = 2a+5 = 5 2a Thus 2a 5 5 2a = 2a 5 1(2a 5) = ˘˘ (2a˘˘5) 1˘(2˘a˘˘5) = 1 1 ...
PDF Solving Rational Equations
Solve rational equations. Use rational equations to solve real-life problems, such as finding how to dilute an acid solution in Example 5. To solve real-life problems, such as finding the year in which a certain amount of rodeo prize money was earned in Example 6. Why you should learn it GOAL 2 GOAL 1 What you should learn 9.6 R E A L L I F E ...
PDF 8 Solving Rational Equations
Solving Rational Equations Solve the following equations using the LCD to clear fractions first. Note: You must check all answers. 1. 5 9 4 3 1 x + = 2. 6 1 5 3 1 − = x 3. 3x 7 5 1 3 2 − = 4. 3 1 2 1 6 2 + = x
PDF 6.6 Rational Equations and Problem Solving
2 Solving Number Problems Modeled by Rational Equations Problem solving sometimes involves modeling a described situation with an equation containing rational expressions. In Examples 2 through 5, we practice solving such problems and use the problem-solving steps first introduced in Section 2.2. EXAMPLE 2 Finding an Unknown Number
PDF Practice Worksheet: Solving Rational Equations
Practice Worksheet: Solving Rational Equations Solve each equation and check for extraneous solutions. You must show work and your answers must be correct to get credit. Level 1 Level 2 Level 3 1] 5] 9] 2] 6] 10] 3] 7] 11] 4] 8] 12] Level 4 Level 5 (Extra Credit) 13] 16] 14] 17] 15] 18] Author: Robyn Wolfe ...
PDF Chapter 9: Rational Expressions and Equations
variation problems. • Lesson 9-5 Identify graphs and equations as different types of functions. • Lesson 9-6 Solve rational equations and inequalities. Rational expressions, functions, and equations can be used to solve problems involving mixtures, photography, electricity, medicine, and travel, to name a few.
16-week Lesson 11 (8-week Lesson 9) Solving Rational Equations 2 Steps for Solving Rational Equations: 1. factor all denominators 2. multiply both sides of the equation by the least common multiple of all the denominators to eliminate the fractions 3. distribute and combine like terms 4. isolate the variable
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Word Problems that use Rational Expressions Example: Underground pipes can fill a swimming pool in 4 hours. A regular garden hose can fill the pool in 15 hours. If both are used at the same thne, how long will it take to fill the pool? Solving Rational Equalities/Equations Step 3: Check Answer! If time is 3.158 hours, the pipes will add
Application Problems with Rational Expressions The applications will involve situations with work rate, variations, water current and speed of wind. Work rate Work rate problems usually involve two people that are trying to help each other finish a single job. Fran can clean the garage in 3 hours, but it takes Angie 4 hours to do the same job.
Lecture Notes Rational Expressions page 4 Sample Problems Œ Solutions 1. Simplify each of the following. a) 2a 5 5 2a Solution: We need to notice that the numerator and denominator are opposites of each other. Indeed, the opposite of 2a 5 is 5 2a since 1(2a 5) = 2a+5 = 5 2a Thus 2a 5 5 2a = 2a 5 1(2a 5) = ˘˘ (2a˘˘5) 1˘(2˘a˘˘5) = 1 1 ...
Solve rational equations. Use rational equations to solve real-life problems, such as finding how to dilute an acid solution in Example 5. To solve real-life problems, such as finding the year in which a certain amount of rodeo prize money was earned in Example 6. Why you should learn it GOAL 2 GOAL 1 What you should learn 9.6 R E A L L I F E ...
Solving Rational Equations Solve the following equations using the LCD to clear fractions first. Note: You must check all answers. 1. 5 9 4 3 1 x + = 2. 6 1 5 3 1 − = x 3. 3x 7 5 1 3 2 − = 4. 3 1 2 1 6 2 + = x
2 Solving Number Problems Modeled by Rational Equations Problem solving sometimes involves modeling a described situation with an equation containing rational expressions. In Examples 2 through 5, we practice solving such problems and use the problem-solving steps first introduced in Section 2.2. EXAMPLE 2 Finding an Unknown Number
Practice Worksheet: Solving Rational Equations Solve each equation and check for extraneous solutions. You must show work and your answers must be correct to get credit. Level 1 Level 2 Level 3 1] 5] 9] 2] 6] 10] 3] 7] 11] 4] 8] 12] Level 4 Level 5 (Extra Credit) 13] 16] 14] 17] 15] 18] Author: Robyn Wolfe ...
variation problems. • Lesson 9-5 Identify graphs and equations as different types of functions. • Lesson 9-6 Solve rational equations and inequalities. Rational expressions, functions, and equations can be used to solve problems involving mixtures, photography, electricity, medicine, and travel, to name a few.
Solving Rational Equations Date_____ Period____ Solve each equation. Remember to check for extraneous solutions. 1) 1 6 k2 = 1 3k2 − 1 k {1 6} 2) 1 n2 + 1 n = 1 2n2 {− 1 2} 3) 1 6b2 + 1 6b = 1 b2 {5} 4) b + 6 4b2 + 3 2b2 = b + 4 2b2 {4} 5) 1 x = 6 5x + 1 {− 1 5} 6) 1 6x2 = 1 2x + 7 6x2 {−2} 7) 1 v + 3v + 12 v2 − 5v = 7v − 56 v2 − ...
16-week Lesson 11 (8-week Lesson 9) Solving Rational Equations 2 Steps for Solving Rational Equations: 1. factor all denominators 2. multiply both sides of the equation by the least common multiple of all the denominators to eliminate the fractions 3. distribute and combine like terms 4. isolate the variable