# Thread: How to find Mt and N

1. ## How to find Mt and N

$t^2+4t+3=A(1+t^2)+(Mt+N)2t$
I got that $A=3$
But how do I get $Mt$and $N$

2. Originally Posted by totalnewbie
$t^2+4t+3=A(1+t^2)+(Mt+N)2t$
I got that $A=3$
But how do I get $Mt$and $N$
One way is to expand,
Expand,
$t^2+4t+3=(A+2M)t^2+(2N)t+(A)$
Corresponding parts are equal,
$\left\{ \begin{array}{cccc}A&+2M& \,&=1 \\ \,&\,&N&=4\\ A&\,&\,& = 3 \end{array} \right\}$
You can solve the first equation since you know the third.
Thus,
$\left\{ \begin{array}{c}A=3\\M=-1\\N=4 \end{array} \right\}$