A-Level Maths: B10-08 Algebraic Fractions: How we deal with Repeated Factors in the Denominator

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[@TLMaths]

Glad it was helpful!

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For the videos that are entitled “extension” do they feature in the A level course?

[@TLMaths]

No, they are purely for extension

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Thank u so much sir

[@jacobridley8156]

thanks sir

[@aafroditii]

I do not understand why in the example you used B/x+2. Where did the x+2 come from, it was x+2^2 in the original denominator so shouldnt it be A/x-1) +B/(x+2)+ C/(x+2)+ D/x+2^2 ?

[@TLMaths]

But A/(x-1) + B/(x+2) + C/(x+2) + D/(x+2)^2 can be written as
A/(x-1) + (B+C)/(x+2) + D/(x+2)^2
which can be written as
A/(x-1) + E/(x+2) + D/(x+2)^2
which is just the same as using
A/(x-1) + B/(x+2) + C/(x+2)^2

[@Ninjaah_]

What would you do if a factor in the denominator is x^2 ?

[@TLMaths]

Same deal. 1/((x-1)*x^2) = A/(x-1) + B/x + C/x^2

[@Ninjaah_]

@@TLMaths but if you multiply it all out by (x-1)(x^2) and let x = 0 and x=1, you’d only get 2 terms? how would you get the last one?

[@TLMaths]

Choose another value of x that you haven't used.

[@Doodo981]

Do we have to do (x+2)^2 for C or can we do C for x+2 ?

[@Doodo981]

As a repeated dominator

[@TLMaths]

You need to have something over (x-1) + something over (x+2) + something over (x+2)^2

[@hanmoj31]

shouldnt it be cx+d/(x+2)^2 instead of c/(x+2)^2 ?

[@TLMaths]

No, but you could just consider A/(x-1) + (Bx+C)/(x+2)^2 but that’s not as helpful as A/(x-1) + B/(x+2) + C/(x+2)^2

[@hanmoj31]

@@TLMaths ohhh got it, thanks sir

[@Mostpeoplecant]

cheers

[@taegan9751]

Why couldn't (x-1)(x+2) have been a possible factor for the denominator?

[@TLMaths]

You only want single linear terms in the denominator for partial fractions

[@taegan9751]

@@TLMaths Thanks for your reply. Sorry if this is a silly question, but why is that?

[@TLMaths]

Because you're trying to write your rational function as the sum of partial fractions, possibly in order to integrate or use binomial expansion. Either way, this is made simpler by having single brackets in the denominator.

[@taegan9751]

@@TLMaths Ahh thank you that makes sense!

[@misan2002]

I don't understand the part where you talked about other fractions

[@legendlegend4459]

5:25 I don't understand why you got 3 and 4 as the denominator

[@TLMaths]

I'm using factors of 24

[@nurtaymergaliyev5864]

@@TLMaths the product of 3 and 4 is not 24 though