1. ## Partial fractions

1. a) Express (x+3)/x²(x-1) in terms of partial fractions

b) Find ∫(x+3)/x²(x-1)dx

Not sure if i need to expand the denominator in a?

really have no idea how to do b!

2. Originally Posted by djmccabie
1. a) Express (x+3)/x²(x-1) in terms of partial fractions

b) Find ∫(x+3)/x²(x-1)dx

Not sure if i need to expand the denominator in a?

really have no idea how to do b!
$\frac{x+3}{x^2(x-1)}$

$= \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-1}$

3. Originally Posted by djmccabie
1. a) Express (x+3)/x²(x-1) in terms of partial fractions

b) Find ∫(x+3)/x²(x-1)dx

Not sure if i need to expand the denominator in a?

really have no idea how to do b! that's why you do (a) first
$
\frac{x+3}{x^2(x-1)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-1}
$

$x+3 = Ax(x-1) + B(x-1) + Cx^2$

let $x = 1$ ... $C = 4$

let $x = 0$ ... $B = -3$

let $x = 2$ ... $A = -4$

$\int \frac{x+3}{x^2(x-1)} \, dx = \int -\frac{4}{x} - \frac{3}{x^2} + \frac{4}{x-1} \, dx
$

4. hi just a question. When you let x=2, what happens to B and C ?

5. Replace them with the values you already had: B= -3, C= 4.