Question

Find the general term of the following expressions when expanded in ascending powers of $x$.
$\frac{5x+6}{(2+x)(1-x)}$

Answer 1

To find the general term of the following expressions when expanded in ascending powers of x

$\frac{5x+6}{(2+x)(1-x)}$

Here , we have

$\frac{5x+6}{(2+x)(1-x)}$

The Expression can be written as

$\frac{11}{3(1-x)}-\frac{4}{3(2+x)}$

and the General Term can be written as

$\frac{1}{3}\{11-\frac{(-1{)}^r}{2^{r-1}}\}$