Algebraic Fractions
Overview
An algebraic fraction is just a fraction with letters in it, and the same rules you already know for ordinary fractions still apply. The art is in factorising the top and bottom so that common factors can be cancelled, turning a heavy-looking expression into something clean and simple.
In this lesson you will simplify algebraic fractions by cancelling common factors, then move to the Extended skills of adding, subtracting, multiplying and dividing them, and of factorising and simplifying rational expressions. These techniques are the workhorses behind solving equations and rearranging formulas later in the course.
Objectives
- 1 Simplify algebraic fractions.
- Manipulate algebraic fractions. (Extended only)
- Factorise and simplify rational expressions. (Extended only)
Audio Lesson
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Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Algebraic Fractions. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Simplify 6x^2 / 9x. A. 2x/3 B. 3x/2 C. 2/(3x) D. 6x/9 Answer: A
- Simplify (x^2 - 9) / (x^2 + 5x + 6). A. (x-3)/(x+2) B. (x+3)/(x+2) C. (x-3)/(x-2) D. x - 3 Answer: A
- Express 2/x + 3/(x+1) as a single fraction. A. 5/(2x+1) B. (5x+2)/(x(x+1)) C. 6/(x(x+1)) D. (5x-2)/(x(x+1)) Answer: B
- Simplify (x/4) divided by (x^2/8). A. x/2 B. 2/x C. x^3/32 D. 8/(4x) Answer: B
- Which of these may be cancelled in a fraction? A. An added term B. A subtracted term C. A common factor D. Any letter Answer: C
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