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Simplifying Algebraic Fractions and Solving Equations

Learn how to simplify algebraic fractions and solve equations involving quadratic and linear functions. Step-by-step examples provided.

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Simplifying Algebraic Fractions and Solving Equations

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  1. Unit 25Solving Equations

  2. Unit 25Solving Equations 25.1 Algebraic Fractions

  3. You can sometimes simplify fractions when the numerator and denominator are factorial. Example Simplify ? ? ? ? ? ? ? ? ?

  4. Unit 25Solving Equations 25.2 Algebraic Fractions and Quadratic Equations

  5. Example Solve Multiply both sides by to give Solution First combine the two fractions on the LHS by putting them over a common denominator. ? ? ? ? ? ? ? ? ? Simplify to give Divide each term by 4 Factorise Either or So or ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

  6. Unit 25Solving Equations 25.3 Solving Simultaneous Equations: One Linear and One Quadratic

  7. 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 Solution You can eliminate y by taking one equation from the other to give or ? This is a quadratic that can be factorised to give ? ? Either or etc. or So ? ? or and ? ?

  8. Unit 25Solving Equations 25.4 Note

  9. Note The 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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