method of difference question (fp2)

I have come across a question with more then two terms per line and am not sure how to cancel them down? I have cancelled the like terms but am still left with way too many terms and not sure what I've done wrong

can someone point me in the right direction

paper (question 5)
https://8dedc505ac3fba908c50836f59059ccce5cd0f1e.googledrive.com/host/0B1ZiqBksUHNYdHIxUkJmdndfMlE/June%202013%20(Withdrawn)%20QP%20-%20FP2%20Edexcel.pdf

They don't quite cancel in the way that you make it out to be in your working.

+1/3 doesn't cancel out +1/3, but +1/3 and +1/3 cancels out -2/3 for example.

and +1/4 + 1/4 cancels out -1/2 and so on?

Yes.

Anyone know if cancellations like these are common in exams? Or is it usually quite simple?

Anyone know if cancellations like these are common in exams? Or is it usually quite simple?

Anyone know if cancellations like these are common in exams? Or is it usually quite simple?

It's usually like this; it takes a little bit of observation sometimes but that's really all you need

Yes, they come up annoyingly. Dunno about IAL.

I'm sure they'll find a way to make them difficult But seriously, keep a cool head, write out the first few terms in a nice block, as well as the last few terms in terms of n and then see what should cancel out and you should be fine.

What paper is this?

June 2013 (Withdrawn).

Hey Zain, do you think I'd get method marks for splitting up partial fractions using algebra (adding in zeroes) instead of comparing coefficients?

June 2013 (Withdrawn).

Hey Zain, do you think I'd get method marks for splitting up partial fractions using algebra (adding in zeroes)

What do you mean? Give me an example.

Any method that works should be OK. Students from the Far East (e.g Singapore) often solve 3 by 3 simultaneous equations because they are so slick at it.

What do you mean? Give me an example.

Any method that works should be OK. Students from the Far East (e.g Singapore) often solve 3 by 3 simultaneous equations because they are so slick at it.

Have you ever seen the "shoelace" formula while marking pure scripts? I use that formula to find areas in coordinate geometry problems because that's what we were taught to use the year before our IGCSEs.

Something along these lines rather than comparing coefficients:

$\displaystyle \frac{3x+2}{x^{2}+x} = \frac{3x + 2}{x\left ( x+1 \right )}= \frac{x+2x+2}{x\left ( x+1 \right )}=\frac{x+2\left ( x+1 \right )}{x\left ( x+1 \right )}= \frac{x}{x\left ( x+1 \right )}+\frac{2\left ( x+1 \right )}{x\left ( x+1 \right )} = \frac{1}{x+1}+\frac{2}{x}$


$\displaystyle \therefore \frac{3x+2}{x^{2}+x}\equiv \frac{1}{x+1}+ \frac{2}{x}$

This is the exact amount of working I'd show on paper.

Haha, a lot of Eastern students do have interesting methods of doing problems! I've seen people doing M2/3 stuff using cool vector methods! Have you ever seen the "shoelace" formula while marking pure scripts? I use that formula to find areas in coordinate geometry problems because that's what we were taught to use the year before our IGCSEs.