Alg5.1.3

Write as sum of partial fractions $\frac{3x}{(x+1)(x-2)}\,$

Let $\frac{3x}{(x+1)(x-2)}= \frac{A}{x+1}+\frac{B}{x-2}\,$

Multiply all terms on both sides by the common denominator $(x+1)(x-2)\,$ .

$3x = A(x-2) + B(x+1)\,$

So if $x=2\,$

then $6=3B\,$ .

Therefore $B=2\,$ .

Similarly if $x=-1\,$

then $-3=-3A\,$ .

Therefore $A=1\,$ .

So $\frac{3x}{(x+1)(x-2)} = \frac{1}{x+1} + \frac{2}{x-2}\,$