From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 .../concept/partial-fraction-decomposition/index.md  | 20 ++++++++++----------
 1 file changed, 10 insertions(+), 10 deletions(-)

(limited to 'source/know/concept/partial-fraction-decomposition/index.md')

diff --git a/source/know/concept/partial-fraction-decomposition/index.md b/source/know/concept/partial-fraction-decomposition/index.md
index 03c1c76..bb7faa2 100644
--- a/source/know/concept/partial-fraction-decomposition/index.md
+++ b/source/know/concept/partial-fraction-decomposition/index.md
@@ -8,15 +8,15 @@ layout: "concept"
 ---
 
 **Partial fraction decomposition** or **partial fraction expansion**
-is a method to rewrite quotients of two polynomials $g(x)$ and $h(x)$,
-where the numerator $g(x)$ is of lower order than $h(x)$,
-as sums of fractions with $x$ in the denominator:
+is a method to rewrite quotients of two polynomials $$g(x)$$ and $$h(x)$$,
+where the numerator $$g(x)$$ is of lower order than $$h(x)$$,
+as sums of fractions with $$x$$ in the denominator:
 
 $$\begin{aligned}
     f(x) = \frac{g(x)}{h(x)} = \frac{c_1}{x - h_1} + \frac{c_2}{x - h_2} + ...
 \end{aligned}$$
 
-Where $h_n$ etc. are the roots of the denominator $h(x)$. If all $N$ of
+Where $$h_n$$ etc. are the roots of the denominator $$h(x)$$. If all $$N$$ of
 these roots are distinct, then it is sufficient to simply posit:
 
 $$\begin{aligned}
@@ -25,8 +25,8 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-The constants $c_n$ can either be found the hard way,
-by multiplying the denominators around and solving a system of $N$
+The constants $$c_n$$ can either be found the hard way,
+by multiplying the denominators around and solving a system of $$N$$
 equations, or the easy way by using this trick:
 
 $$\begin{aligned}
@@ -35,7 +35,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-If $h_1$ is a root with multiplicity $m > 1$, then the sum takes the form of:
+If $$h_1$$ is a root with multiplicity $$m > 1$$, then the sum takes the form of:
 
 $$\begin{aligned}
     \boxed{
@@ -44,15 +44,15 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where $c_{1,j}$ are found by putting the terms on a common denominator, e.g.
+Where $$c_{1,j}$$ are found by putting the terms on a common denominator, e.g.
 
 $$\begin{aligned}
     \frac{c_{1,1}}{x - h_1} + \frac{c_{1,2}}{(x - h_1)^2}
     = \frac{c_{1,1} (x - h_1) + c_{1,2}}{(x - h_1)^2}
 \end{aligned}$$
 
-And then, using the linear independence of $x^0, x^1, x^2, ...$, solving
-a system of $m$ equations to find all $c_{1,1}, ..., c_{1,m}$.
+And then, using the linear independence of $$x^0, x^1, x^2, ...$$, solving
+a system of $$m$$ equations to find all $$c_{1,1}, ..., c_{1,m}$$.
 
 
 
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