$\"\"$

\

The partial fraction of decomposition rational expression is $\"\"$ .

\

Rewrite the expression into partial fraction.

\

$\"\"$

\

Find the values of $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

Multiple each side by the denominator fraction.

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Equate the coefficent of $\"\"$ , $\"\"$ , $\"\"$ and constants.

\

$\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

$\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute the $\"\"$ in $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Therefore $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\

Substistute the $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ values in equation $\"\"$ .

\

$\"\"$

\

The partial decomposed function is $\"\"$ .

\

$\"\"$

\

Graph :

\

Graph the functions $\"\"$ and $\"\"$ .

\

$\"\"$

\

Observe the graph

\

$\"\"$ .

\

$\"\"$

\

The partial decomposed function is $\"\"$ .