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math117: fix pfd directions

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eggy 2022-09-26 11:13:05 -04:00
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@ -170,12 +170,13 @@ Please see [SL Physics 1#6.1 - Circular motion](/g11/sph3u7/#61-circular-motion)
In order to PFD: In order to PFD:
1. Factor the denominator into irreducibly quadratic or linear terms. 1. Factor the denominator into *irreducibly* quadratic or linear terms.
2. For each factor, create a term. Where capital letters below are constants: 2. For each factor, create a term. Where capital letters below are constants:
- A linear factor $Bx+C$ has a term $\frac{A}{Bx+C}$. - A linear factor $Bx+C$ has a term $\frac{A}{Bx+C}$.
- A quadratic factor $Dx^2+Ex+G$ has a term $\frac{H}{Dx^2+Ex+G}$. - An *irreducibly* quadratic factor $Dx^2+Ex+G$ has a term $\frac{Hx+J}{Dx^2+Ex+G}$.
3. Set the two equal to each other such that the denominators can be factored out. - Duplicate factors have terms with denominators with that factor to the power of 1 up to the number of times the factor is present in the original.
4. Create systems of equations to solve for each constant. 4. Set the two equal to each other such that the denominators can be factored out.
5. Create systems of equations to solve for each constant.
!!! example !!! example
To decompose $\frac{x}{(x+1)(x^2+x+1)}$: To decompose $\frac{x}{(x+1)(x^2+x+1)}$: