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2. 2. +. = 6. x-2. x+1. 2 (x+1) + 2 (x-2). = 6. (x-2) (x+1). (x-2) (x+1). 2(x+1) + 2(x-2) = 6 4x + 2 + 4x – 4 = 6 (x ²-x-2) 8x -2 = 6x² -6x -12 0 = 6 x² - 14x - 10 3x² - 7x - 5 = 0. Multiply out those brackets!. OOH! – I could make those numbers easier to work with.

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  1. 2 2 + = 6 x-2 x+1 2(x+1) + 2(x-2) = 6 (x-2)(x+1) (x-2)(x+1) 2(x+1) + 2(x-2) = 6 4x + 2 + 4x – 4 = 6 (x²-x-2) 8x -2 = 6x² -6x -12 0 = 6x² - 14x - 10 3x² - 7x - 5 = 0 Multiply out those brackets! OOH! – I could make those numbers easier to work with Now solve that quadratic!

  2. x 2 = ½ + x-2 x+1 2(x+1) + x(x-2) = ½ (x-2)(x+1) 2(x+1) + x(x-2) = ½ 4x + 2 + x² – 2x = ½ (x²-x-2) 2(x² +2x + 2) = 1(x² - x – 2) 2x² + 4x + 4 = x² - x - 2 x² + 5x +6 = 0 (x-2)(x+1) Multiply out those brackets! Deal with that fraction! Now solve that quadratic!

  3. 4 x = 6 x-2 x+1 x(x+1) - 4(x-2) = 6 (x-2)(x+1) (x-2)(x+1) x(x+1) - 4(x-2) = 6 x² + x - 4x + 8 = 6 (x²-x-2) x² - 3x + 8= 6x² -6x -12 0 = 5x² - 3x - 20 Multiply out those brackets – watch out for that negative sign! Now solve that quadratic!

  4. 4 x+3 + = 6 x²-9 x+1 2(x+1) + 2(x²-9) = 6 (x²-9)(x+1) EEK! – THIS WILL MULTIPLY OUT TO MAKE A CUBIC! – WE NEED TO AVOID THIS. LET’S START AGAIN!

  5. 4 x+3 - = 6 x²-9 x+1 LET’S FACTORISE! x+3 4 - = 6 x+1 (x+3)(x-3) 1 4 - = 6 (x-3) x+1 Multiply out those brackets – watch out for those negative signs! (x+1) - 4(x-3) = 6 (x-3)(x+1) Quadratic to solve is 0 = 6x² - 9x – 31 (x-3)(x+1) = 6 (x+1) - 4(x-3) x + 1 - 4x +12 = 6(x²-3x+x-3)

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