Please show working to express these in partial fractions

• Nov 18th 2009, 07:58 AM
malteseboy
Please show working to express these in partial fractions
Express in partial fractions:

a) (3x + 1) / (x + 1)^2

b) (x^2 + 7x + 2) / (1 + x^2)(2 - x)
• Nov 18th 2009, 03:47 PM
skeeter
Quote:

Originally Posted by malteseboy
Express in partial fractions:

a) (3x + 1) / (x + 1)^2

b) (x^2 + 7x + 2) / (1 + x^2)(2 - x)

$\displaystyle \frac{3x+1}{(x+1)^2} = \frac{A}{x+1} + \frac{B}{(x+1)^2}$

$\displaystyle \frac{x^2+7x+2}{(1+x^2)(2-x)} = \frac{Ax+B}{1+x^2} + \frac{C}{2-x}$
• Nov 18th 2009, 03:53 PM
pencil09
Quote:

Originally Posted by malteseboy
Express in partial fractions:

a) (3x + 1) / (x + 1)^2

b) (x^2 + 7x + 2) / (1 + x^2)(2 - x)

a)
$\displaystyle \frac {3x + 1} {(x + 1)^2}$ (it's the repeated factor type) so
$\displaystyle \frac {3x + 1} {(x + 1)^2}=\frac {A}{x+1}+\frac {B}{(x+1)^2}$
$\displaystyle \frac {3x + 1} {(x + 1)^2}=\frac {A(x+1)+B}{(x+1)^2}$
you can cancel the denominator,
so you have
$\displaystyle 3x + 1=A(x+1)+B$
you just have to find the value for A and B and then change A and B from this eq...$\displaystyle \frac {A}{x+1}+\frac {B}{(x+1)^2}$

....hope it help.....(Nod)