# Math Help - partial fractions and binomial expansion

1. ## partial fractions and binomial expansion

I have expressed the expression as partial fractions and I have done binomial expansion up to x cubed. The answer in the book has different coefficients of x squared and x cubed. I have had a good look at it. Can someone check it?

2. I got +1/2 as the numerator of 1/(2-x).

Check this one again.

EDIT: I took the wrong denominator, that is 1/(x-2). Problem resolved later.

3. I can't find any mistake with the partial fractions. It checks ok when reversed.

4. Oh right. Sorry, I was using 1/(x-2)

In your simplification line of the first term.

$\dfrac{-1.-2}{2!} \left(\dfrac{x}{4}\right)^2 \neq \dfrac{3x^2}{32}$

$\dfrac{-1.-2}{2!} \left(\dfrac{x}{4}\right)^2 = \dfrac{x^2}{16}$

The binomial coefficient is not to add the numerator but to multiply them.

5. Yes its a simpler mistake than I was expecting. I am only used to positive integral powers.