Question

Find the partial fraction decomposition for the rational expression.
15x-21
OVER
x^2-3x+2

Answer 1

x^2-3x+2 can be factored

Answer 2

? what?

Answer 3

Factor \(x^2 - 3x + 2\) into \((x-2)(x-1)\)

Answer 4

o how u knoow how to do that

Answer 5

Practice

Answer 6

how did u do that ha

Answer 7

\[(x + a)(x + b) = x^2 + (a+b)x + ab\]
Therefore you are looking for an a and b such that:
\[a+b = -3 \text{ and } a\cdot b = 2\]

Answer 8

ok

Answer 9

still not done yes

Answer 10

\[\frac{15x-21}{(x-2)(x-1)}=\frac{A}{x-2}+\frac{B}{x-1}\]

Answer 11

\[A=\frac{15\times 2-21}{(2-1)}=9\]

Answer 12

\[B=\frac{15\times 1-21}{1-2}=6\]

Answer 13

answer is
\[\frac{15x-21}{(x-2)(x-1)}=\frac{9}{x-2}+\frac{6}{x-1}\]