A-Level Maths: B10-03 Algebraic Fractions: Introducing Partial Fractions via Substitution

[operationfigures]

GIVE THIS MAN A MEDAL. Wish you were my maths teacher, sad how I've learnt more from a random person on youtube than someone who is paid to teach me :( lol

[ozakki]

I’m currently doing final year BEng in Engineering after 12 years out of the education game. I’ve learned everything again but one thing I’ve struggled with is partial fractions as part of Laplace Transforms etc. I’ve read books, asked my own Lecturer, watched videos, but nothing has stuck until watching this. Thank you so much for breaking it down so well!

[learnenglishwithjulie]

These videos are absolutely brilliant - thanks so much 😃👏🏼

[Nilsy]

Amazing Jack thank you for the clear explanation as usual. Just one question: Why is it valid to substitute 3 and 2 as X when it will result in you dividing by zero on the first line?
Does this not raise doubt as to the validity of A and B if when we substitute 3 and 2 back into the original equation we are dividing by zero? Hope the question makes sense.

[misan]

can you explain the part where you solve for a and b again? please
thank you

[aidenstonehouse]

Question. Why do we assume that the initial fraction is composed of just two fractions here. I know based on the examples in your other videos, it so happens that you can express the fraction as two parts. But we express these fractions as two parts because when we mess around with these two parts we get a fraction with the same denominator. But for this example, expressing the fraction as a/x-3 + b/x-2 + 1/c would also get us the same denominator. But now we have a different numerator to just a/x-3 + b/x-2. Why is the one the correct assumption and the other not, as both will produce the same denominator but one has an extra term?

Is it because if we express 7x-16/(x-3)(x-2) as being identical to a/x-3 + b/x-2 + c/1 if we then re-arrange this to get the common denominator, it would be now show as an improper fraction? If you then solve as normal we find c=0, so its clear c/1 did'nt need to be there, but why because the it fits the first step of logic.

[naturalbby]

Love your videos! Thanks for your help

[joshuacarpenter]

I'm a year 11, who is hopefully doing A level Maths next academic year. So have the exam boards moved away from the 4 core modules now as I am a bit confused.

[QasimAli-cfln]

My exam board is edexcel and they use the comparing method. I was wondering if it was alright for me to use this method in the exam?

[cakesnstrawberrys]

at 3:48 you put a plus between the two separated fractions eventhough there's a - between 7x-16 . Can you please explain this concept? Thankyou.

[rasheede.o]

I am in Year 12. When I was solving the partial fraction 3x+9/x^3-36x I noticed I got B=3/8
and C= -1/8.
The correct answers are B=-1/8 and C= 3/8.

I don't understand why I got different answers. Does the ordering of the linear factors matter