From 62ce58eb8bddd8d67e5c1f875d2ec1238b4f5f5d Mon Sep 17 00:00:00 2001 From: zleyyij Date: Wed, 14 Feb 2024 09:15:34 -0700 Subject: [PATCH] vault backup: 2024-02-14 09:15:34 --- education/math/Partial Fractions.md | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/education/math/Partial Fractions.md b/education/math/Partial Fractions.md index 4341eb5..484f9d3 100644 --- a/education/math/Partial Fractions.md +++ b/education/math/Partial Fractions.md @@ -1,8 +1,16 @@ +Partial fraction decomposition is when you break a polynomial fraction down into smaller fractions that add together. ## Degree where the numerator is less 1. Factor the bottom. -2. Create two fractions, a/p1, and b/p2, where p1 and p2 are the polynomials you just factored out, and a/b are arbitrary variables +2. Create two fractions, $\frac{a}{p1}$, and $\frac{b}{p2}$, where p1 and p2 are the polynomials you just factored out, and a/b are arbitrary variables 3. Multiply a by p2, and b by p1., giving you: $$\frac{a*p2}{p1} + \frac{b*p1}{p2}$$ 4. When you split the + +### Example +$$ \frac{2x+1}{(x+1)(x+2)} $$ +Given the above fraction, the denominator is already factored, so we can move onto the next step, where two fractions are made with $a$ and $b$ in the numerator, and each of the denominator components in the denominator: +$$ \frac{a}{x+1} + \frac{b}{x+2} $$ +Next, find a common denominator so that you can add the two fractions together. In this case, it's $(x+1)(x+2)$. + ## Degree of the numerator is equal 1. First perform polynomial division. 2. Then find a partial fraction with the remainder