Find , where
I know that you need to use partial fractions to integrate this but im having trouble finding the partial fractions. Could someone point me in the right direction? Cheers.
Factorise the denominator to :
$\displaystyle (y+6)(y-3)$
So you have:
$\displaystyle \frac{4y-10}{(y+6)(y-3)} = \frac{A}{y+6} + \frac{B}{y-3} $
Now multiply through by $\displaystyle (y+6)(y-3)$
$\displaystyle 4y-10 = A(y-3)+ B(y+6) $
$\displaystyle 4y-10 = Ay-3A+ By+6B $
Now compare coefficients of $\displaystyle y$ and $\displaystyle 1 $:
$\displaystyle 4y = Ay + By$
$\displaystyle \therefore A+B = 4$
$\displaystyle -10 = -3A + 6B$
Solve by simultaneous equations!