The inverse of 1-x2 can be calcuated two ways.
First way: We know 1/(1-y)=(1+y+y2+y3+...) so substitute y=2x, and it comes out.
Second way: Do it directly.
- The constant coefficent must be 1.
- The x coefficient must 2.
- The x2 coefficient must 4.
- The x3 coefficient must 8.
We did a couple more examples of computing an inverse. Then we went to an interesting one.
What is the multiplicative inverse of 1-x-x2.
It turns out to be 1+x+2x2+3x3+5x4+8x5+13x6...
The coefficients are the fibonacci series!