Fun challenge question actually quite difficult!

basically it starts as follows:

Express 2 / ((2-x) (1-x)) as partial fractions

so i got (2/1-x) - (2/2-x)

I then made this into 2((1-x)^(-1) - (2-x)^-1)

However it says. Show that for small values of x the original expression is equal to 1 + kx + 7/4x^2

I understand this is binomial expansion and the first expansion (1-x) is

1-x+x^2? Is this correcT?

If so, can someone remind me how to binomially expand the second one and get towards the answer? :smile:

Reply 1

MathMan

6

Factor the two out of the bracket and raise the remaining factor it to the power of -1/2, remember you can only use the general binomial theorem when the monomial your expanding is in the form (1-ax)^n, so if its not in this form you have to factor out a constant.

Reply 2

user121

OP

2

Original post by MathMan

Factor the two out of the bracket and raise the remaining factor it to the power of -1/2, remember you can only use the general binomial theorem when the monomial your expanding is in the form (1-ax)^n, so if its not in this form you have to factor out a constant.