Express f(x)=2x+2x2−2x−3−x+1x−3\displaystyle f(x) = \frac{2x+2}{x^2-2x-3} - \frac{x+1}{x-3}f(x)=x2−2x−32x+2−x−3x+1 as a single fraction in its simplest form.
Hence show that f′(x)=2(x−3)2\displaystyle f'(x) = \frac{2}{(x-3)^2}f′(x)=(x−3)22.
Practise Edexcel A Level Old Maths Differentiation with exam-style questions for A Level Old Maths. 14 questions, matched to the Edexcel A Level Old Maths (9371) specification and written in Unit exams C1, C2, C3 and C4 plus two applied units (e.g. S1 and M1) style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.