From f186e4045867d1684139293f5d4d3e65180bf853 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Wed, 14 Feb 2024 10:02:53 -0700 Subject: [PATCH] vault backup: 2024-02-14 10:02:53 --- education/math/Partial Fractions.md | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/education/math/Partial Fractions.md b/education/math/Partial Fractions.md index bc8e56c..27d9594 100644 --- a/education/math/Partial Fractions.md +++ b/education/math/Partial Fractions.md @@ -4,7 +4,7 @@ This is the "main" method of solving, and the next two headings both focus on ge 1. Factor the bottom. 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 +4. Now you can distribute $a$ and $b$, giving you $ax + c$ and $bx + d$. Group and factor. Your equation equals the original equation, so the numerator of the first equals $ax + bx + c + d$. ### Example $$ \frac{2x+1}{(x+1)(x+2)} $$ @@ -24,7 +24,10 @@ $$ 2x+1 = x(a + b) + (2a + b) $$ 7. With the above equation, each side is in the same form. it's $x$ multiplied by a constant ($2$ on the left, and $(a+b)$ on the right, and with a constant of $1$ on the left and $2a + b$) on the right, letting you find the two equations below: $$ 2 = a + b $$ $$ 1 = 2a + b $$ -8. The above equations can be solved as a system of equations, giving you +8. The above equations can be solved as a system of equations, giving you: +$$ a=-1,\space b=3 $$ +9. Your answer would be: + $$ \frac{-1}{x+1} + \frac{3}{x+2} $$ ## Degree of the numerator is equal 1. First perform polynomial division.