Year 11 Exam > Year 11 Notes > Mathematics for GCSE/IGCSE > Solving Algebraic Fractions
Solving Algebraic Fractions | Mathematics for GCSE/IGCSE - Year 11 PDF Download
How do I solve an equation that contains algebraic fractions?
There are two approaches for solving equations containing algebraic fractions:
- In the first method, you handle the algebraic fractions by adding or subtracting them first, and then proceed to solve the equation. This follows the rules for solving linear equations with fractions on one or both sides. Initially, remove the fractions by multiplying both sides by the entire denominator. It's crucial to enclose any expression that you multiply by in brackets.
- The second method involves initially multiplying everything in the fraction by each of the expressions on the denominator. This action eliminates the denominators of the fractions, resulting in either a linear or quadratic equation to solve. Multiplying everything in the fraction by the common denominator is a way to perform this process efficiently in one step.
- For example, to solve the equation
you will need to multiply every term in the equation by both (x - 3) and (x + 1)- STEP 1: Multiply every term by (x - 3)
- STEP 2: Multiply every term by (x + 1)
- STEP 3: Expand the brackets on both sides and simplify
- STEP 4: Rearrange the equation so that it is in a form that can be solved
- STEP 5: Solve the equation
- You can swap the sides if it makes solving the equation easier
- You can swap the sides if it makes solving the equation easier
- STEP 1: Multiply every term by (x - 3)
you will need to multiply every term in the equation by both (x - 3) and (x + 1)
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FAQs on Solving Algebraic Fractions - Mathematics for GCSE/IGCSE - Year 11
| 1. How do I simplify algebraic fractions before solving an equation? |  |
Ans. To simplify algebraic fractions, factorize the numerator and denominator, cancel out any common factors, and then multiply out any remaining terms to simplify the fraction.
| 2. Can I cross multiply when solving equations with algebraic fractions? | |
Ans. Yes, you can cross multiply when solving equations with algebraic fractions. This helps in getting rid of the fractions and solving the equation more efficiently.
| 3. What should I do if I encounter a variable in the denominator of an algebraic fraction when solving an equation? | |
Ans. If you have a variable in the denominator of an algebraic fraction, multiply both sides of the equation by the denominator to eliminate the fraction and solve for the variable.
| 4. Is it important to check for extraneous solutions when solving equations with algebraic fractions? | |
Ans. Yes, it is crucial to check for extraneous solutions when solving equations with algebraic fractions. Sometimes solutions may not satisfy the original equation due to restrictions from the algebraic fractions.
| 5. How can I practice solving equations with algebraic fractions effectively? | |
Ans. Practice solving a variety of equations with algebraic fractions, starting with simpler ones and gradually moving to more complex ones. Use online resources, textbooks, and practice problems to improve your skills in solving these types of equations.
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Dec 18, 2024 Last updated |
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