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Unit 25Solving Equations
Presentation 1 Algebraic Fractions
Presentation 2 Algebraic Fractions and Quadratic Equations
Presentation 3 Solving Simultaneous Equations:One Linear and One Quadratic
Presentation 4 Note
Unit 25Solving Equations
25.1 Algebraic Fractions
You can sometimes simplify fractions when the numerator and denominator are factorial.
Example
Simplify
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Unit 25Solving Equations
25.2 Algebraic Fractions and Quadratic Equations
Solution
First combine the two fractions on the LHS by putting them over a common denominator.
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Simplify to give
Divide each term by 4
Factorise
Either or
So or
ExampleSolve
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Multiply both sides by to give
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Unit 25Solving Equations
25.3 Solving Simultaneous Equations:One Linear and One Quadratic
To solve simultaneous equations when one is linear and one quadratic, you have to first eliminate one variable. You can do this by substituting one of the variables from the linear equation into the quadratic equation, forming a new quadratic in just one variable.
Example
Solve the simultaneous equation This is a quadratic that can be factorised to give
Solution
You can eliminate y by taking one equation from the other to give
or
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So or
and or ?
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Either or etc.
Unit 25Solving Equations
25.4 Note
NoteThe solution , or , are
in fact the points of intersection of the line
with the quadratic function
This is shown in the graph below
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