Question

Write the partial fraction decompression for the rational expression (2X + 5)/(x^2 -x -2)

Answer 1

does the denominator factor?

Answer 2

\[\frac{2x+5}{(x^2-x-2)}=\frac{2x+5}{(x-2)(x+1)}=\frac{A}{x-2}+\frac{B}{x+1}\] i think

Answer 3

you want a quick way to do it?

Answer 4

ya sure

Answer 5

ok lets find A
what makes \(x-2=0\)?

Answer 6

if x was 2

Answer 7

right
now take this
\[\frac{2x+5}{(x-2)(x+1)}\] and put your hand over that factor
\[\frac{2x+5}{\cancel{(x-2)}(x+1)}\]
then replace \(x\) by \(2\) and get
\[\frac{2\times 2+5}{2+1}=\frac{9}{3}=3\]
and so \(A=3\)

Answer 8

oh I get it so B=-1?

Answer 9

for the next one do the same thing, this time use \(x=-1\) and put your hand over the other factor
\[\frac{2x+5}{(x-2)\cancel{(x+1)}}\]

Answer 10

yeah that is it

Answer 11

quick right?

Answer 12

yu

Answer 13

otherwise you write
\[A(x+1)+B(x-2)=2x+5\] and solve for \(A\) and \(B\) but it amounts to the same thing

Answer 14

oops yup. Thanks a lot for your help!

Answer 15

yw