Adding and subtracting rational expressions

0/1

Introduction

Lessons

  1. review – adding/subtracting fractions
0/28

Examples

Lessons

  1. Simplify:
    1. 313+813\frac{3}{{13}} + \frac{8}{{13}}
    2. 32+45\frac{3}{2} + \frac{4}{5}
  2. Simplify:
    1. x6+2x35x4\frac{x}{6} + \frac{{2x}}{3} - \frac{{5x}}{4}
    2. y33+2y+36\frac{{y - 3}}{3} + \frac{{2y + 3}}{6}
    3. 3a532a12\frac{{3a - 5}}{3} - \frac{{2a - 1}}{2}
  3. Simplify:
    1. 5x39+6x3x23\frac{{5x - 3}}{9} + 6x - \frac{{3x - 2}}{3}
    2. 3y1443y63 - \frac{{y - 1}}{4} - \frac{{4 - 3y}}{6}
  4. Adding and Subtracting with Common Denominators
    State any restrictions on the variables, then simplify:
    1. 3x+12x5x\frac{3}{x} + \frac{{12}}{x} - \frac{5}{x}
    2. 6a23a+10a+23a\frac{{6a - 2}}{{3a}} + \frac{{ - 10a + 2}}{{3a}}
    3. 6m6m556m5\frac{{6m}}{{6m - 5}} - \frac{5}{{6m - 5}}
    4. 9x12x38+3x2x3\frac{{9x - 1}}{{2x - 3}} - \frac{{8 + 3x}}{{2x - 3}}
  5. Adding and Subtracting with Different Monomial Denominators
    State any restrictions on the variables, then simplify:
    1. 34m+25m\frac{3}{{4m}} + \frac{2}{{5m}}
    2. 54x76\frac{5}{{4x}} - \frac{7}{6}
    3. 2x310x3x25x\frac{{2x - 3}}{{10x}} - \frac{{3x - 2}}{{5x}}
    4. y13y22y2\frac{{y - 1}}{{3y}} - \frac{2}{{2{y^2}}}
  6. Adding and Subtracting with Different Monomial/Binomial Denominators
    State any restrictions on the variables, then simplify:
    1. x43x+5xx2\frac{{x - 4}}{{3x}} + \frac{{5x}}{{x - 2}}
    2. 53m+214m7\frac{5}{{3m + 2}} - \frac{1}{{4m - 7}}
    3. 6x12x+31x4x+5 \frac{6x-1}{2x+3}-\frac{1-x}{4x+5}
  7. State any restrictions on the variables, then simplify: 1x+25x1+3x\frac{1}{{x + 2}} - \frac{5}{{x - 1}} + \frac{3}{x}
    1. Denominators with Factors in Common
      State any restrictions on the variables, then simplify:
      1. 54x512x\frac{5}{{4x}} - \frac{5}{{12x}}
      2. 43x+9+52x+6\frac{4}{{3x + 9}} + \frac{5}{{2x + 6}}
      3. 3x25x8x2\frac{3}{{{x^2} - 5x}} - \frac{8}{{{x^2}}}
    2. Denominators with Factors in Common
      State any restrictions on the variables, then simplify: 5(x1)(x+3)+4(x+2)(x1)\frac{5}{{\left( {x - 1} \right)\left( {x + 3} \right)}} + \frac{4}{{\left( {x + 2} \right)\left( {x - 1} \right)}}
      1. State any restrictions on the variables, then simplify: xx29+5x3\frac{x}{{{x^2} - 9}} + \frac{5}{{x - 3}}
        1. State any restrictions on the variables, then simplify:
          1. 4x35xx22x3\frac{4}{{x - 3}} - \frac{{5 - x}}{{{x^2} - 2x - 3}}
          2. 3a2a2+5a2+3a+2\frac{3}{{{a^2} - a - 2}} + \frac{5}{{{a^2} + 3a + 2}}
          3. 1x2+4x+44x2+5x+6\frac{1}{{{x^2} + 4x + 4}} - \frac{4}{{{x^2} + 5x + 6}}
        2. State any restrictions on the variables, then simplify: x25x+6x22x3x2+9x+20x2+7x+10\frac{{{x^2} - 5x + 6}}{{{x^2} - 2x - 3}} - \frac{{{x^2} + 9x + 20}}{{{x^2} + 7x + 10}}

          Become a Member to Get More!

          • Easily See Your Progress

            We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.

          • Make Use of Our Learning Aids

            Last Viewed
            Practice Accuracy
            Suggested Tasks

            Get quick access to the topic you're currently learning.

            See how well your practice sessions are going over time.

            Stay on track with our daily recommendations.

          • Earn Achievements as You Learn

            Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.

          • Create and Customize Your Avatar

            Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

          Topic Basics
          When adding and subtracting rational expressions, the denominators of the expressions will dictate how we solve the questions. Different denominators in the expressions, for example, common denominators, different monomial/binomial denominators, and denominators with factors in common, will require different treatments. In addition, we need to keep in mind the restrictions on variables.