AQA A-Level Further Maths D12-14 Rational Functions: Examples of Solving Inequalities

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I don't understand why you can't just make the function equal to three from the start, saving you from drawing the graph. I also don't know why when you draw the graph you can set it equal to the line and multiply by the denominator but when you try to do it algebraically without drawing the graph, you have to square the denominator first?

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