Solving Algebraic Fractions
How do I solve an equation that contains algebraic fractions?
- There are two methods for solving equations that contain algebraic fractions
- One method is to deal with the algebraic fractions by adding or subtracting them first and then solving the equation
- Follow the rules for solving a linear equation containing a fraction on one or both sides
- Remove the fractions first by multiplying both sides by everything on the denominator
- Remember to put brackets around any expression that you multiply by
- Follow the rules for solving a linear equation containing a fraction on one or both sides
- The second method is to begin by multiplying everything in the fraction by each of the expressions on the denominator
- This will remove the denominators of the fractions, leaving you with either a linear or a quadratic equation to solve
- Multiplying everything in the fraction by the common denominator is a way of carrying out this process in one go
- For example, to solve the equation you will need to multiply every term in the equation by both and
- STEP 1
Multiply every term by
- STEP 1
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- STEP 2
Multiply every term by
- STEP 2
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- STEP 3
Expand the brackets on both sides and simplify
- STEP 3
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- STEP 4
Rearrange the equation so that it is in a form that can be solved
- STEP 4
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- STEP 5
Solve the equation- You can swap the sides if it makes solving the equation easier
- STEP 5
Examiner Tip
- Multiplying by both denominators at once can speed up the process, but be careful with the algebra if choosing this technique
Worked example
Show that this equation can be written as .
To clear the fractions, we multiply both sides by the denominators.
We can do this one denominator at a time. We can start by multiplying by .
Now multiply by
Now expand brackets
Collect like terms
Add the terms on the left hand side to the right hand side, to complete the question