## 2002 Winter Diet, Paper 1 Qs 9 & 10

### kr88

Posted 21 April 2005 - 09:34 PM

yeh yeh i know these kind of questions r usually simple but have done both like 5 times each and cant get right answer - so frustrating!

for 9, I have gotten as far as..

=3/ (3/ x+1) +1 = 3/1 / 4/(x+1) = 3/1 X (x+1)/4

=3(x+1) / 4

but, the real answer is 3(x+1) / (x+4)

i know im not far from the answer but i thought i was doing it right!

AND 10,...
i know how to do b), and in a) i know to differentiate the function
2x + 3 + 18/(x-4) to get f'(x) = 2 - 18(x-4)^-2)
however, i eventually simplify this 18x^-2 + 14/16 = 0
either my working is wrong (likely!), or i just dont know how to get the values of x (which are 1 and 7) from this.

pleassse help! xxx

### Mr H

Posted 21 April 2005 - 09:56 PM

From 3/ (3/ x+1) +1 you should solve as follows:

You need to combine the denominator ((3/ x+1) +1) into a single fraction.

To do this express the 1 as (x+1)/(x+1)
(extra brackets here to make it correct in typed format)

Then you get 3/(3/(x+1)+(x+1)/(x+1))

You now have two fractions with the same denominator on the bottom of your fraction. Add then together to get:

3/((3+x+1)/(x+1)) = 3/((x+4)/x+1))

When dividing by a fraction, turn the bottom one upside down and multiply.

= 3 X (x+1)/(x+4)

= 3(x+1) / (x+4)

I am not sure this makes much sense in typed format. I would have done this as a handwritten attachment but I have no memory allowance left to do that.

How did you get on with the P&N Calc Paper circle question?

### Ally

Posted 21 April 2005 - 09:59 PM

I've been gazumped.

Edited by ally, 21 April 2005 - 10:00 PM.

### Mr H

Posted 21 April 2005 - 10:05 PM

From Gazumpee to Gazumper!!

Sorry Ally!

Yours is the same as mine but much better looking.

I'm sure kr88 will understand that one better.

I'm gonna have to get a fancy typewriter too!

### Mr H

Posted 21 April 2005 - 10:10 PM

To answer your second question kr88, your differentiation is OK but when equated to 0, it solves like this:

2-18/(x-4) =0

Rearrange:

2=18/(x-4)

Multiply everything by (x-4) to get:

2(x-4) =18

(x-4) =9

Multiply out bracket:

x -8x+16=9

x -8x+7=0

Which factorises to:

(x-1)(x-7)=0

=> x=1, 7

### kr88

Posted 21 April 2005 - 10:24 PM

what can i say, once again u guys have helped me understand! great thanx much i rly appreciate it.. esp with me posting bout 20 questions a day! well slight exaggeration but ya know.. cheers