Validity involving Binomial C4

I do not get how to do validity, once we expand the expanssion, how do we get the validity ?

The magnitude of the bracket has to be less than 1

thanks for example if the binomial was

4/(2+3x)

I expanded and got
2-3x + 9/2x² - 27/4 ^x3

so then what do I do for validity? do I solve 2+3x=0 to get -2/3 so |2/3|<1 ?

You don't need to expand the bracket for validity.
Just look at the bracket bit.
(2+3x)^-1
now take the two outside the bracket, by dividing everything within the bracket by 2:
(2^-1)(1+1.5x)^-1
Now your bracket is in a more useable form. The magnitude of 1.5x must be smaller than 1:
-1<1.5x<1
therefore:
-2/3<x<2/3

The magnitude of the bracket has to be less than 1

Thank you for your response

Cause in the book they express lie x<|2/3| ?

That is also a correct way of representing -2/3<x<2/3 (assuming you meant x rather than 1 above!). I don't know how to get my laptop to write the modulus symbols (|) though.
EDIT: actually, no. I think the modulus symbols should be around the x not the 2/3:
|x|<2/3

Perfect understood

are you doing c4 in june, because I have a question on mixed execise 3D question 11)a) partial fraction, I THINk the book made a mistake cause it is improper and they did not do the long division /

I'm doing C4 in June, yes OCR MEI though, what exam board are you on? Post the question up with your working for me to have a look at. And there's nothing wrong with improper fractions...

I am doing edexcel No cause the book made a mistake I think they should have used long division first and then apply the partial fraction method


Express (9x²+26x+20)/(1+x)(2+x)²
as partial fractions

I am doing edexcel No cause the book made a mistake I think they should have used long division first and then apply the partial fraction method


Express (9x²+26x+20)/(1+x)(2+x)²
as partial fractions

Long division?!!!
Use the A/1+x + B/2+x + C/(2+x)² method. Show some working so I can suggest where you may be going wrong...

for example ok sub 5 into x and you get 125/98 which means that this is improper, agree or not so far

for example ok sub 5 into x and you get 125/98 which means that this is improper, agree or not so far

No tricks here. imo, it looks like you can go ahead and use your normal methods here. If I say A + B + C, does that help?

It doesn't matter if it is improper...
If it helps, my answer is:
3/(1+x) + 6/(2+x) - 4/ (2+x)² Does this agree with your book's answer or with yours?

for example ok sub 5 into x and you get 125/98 which means that this is improper, agree or not so far

Hi, how are you

Ok, for example , I posted above , if you sub x=5 right into the equation you get improper fraction of 125/98 , agree?

Yes, that what the book says, but some strange reason in my book it mentions if the value on the top (denomintaor) is more than the numerator you use long division

for example this one here they use long division

(3x²-3x-2)/(x-1)(x-2)

do you see where I am getting confused