The inverse of 1-*x*^{2} can be calcuated two ways.

First way: We know
1/(1-*y*)=(1+*y*+*y*^{2}+*y*^{3}+...)
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
*x*^{2}coefficient must 4. - The
*x*^{3}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*-*x*^{2}.

It turns out to be 1+*x*+2*x*^{2}+3*x*^{3}+5*x*^{4}+8*x*^{5}+13*x*^{6}...

The coefficients are the fibonacci series!

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