Question

decompose (-6x)/(x-6)(x+3) into partial fractions

Answer 1

@Directrix

Answer 2

\[\frac{-6x}{(x-6)(x+3)}=\frac{A}{x-6}+\frac{B}{x+3}\] and you need A and B
want to do it the amazingly quick way?

Answer 3

yep i would love to

Answer 4

I'd like to see it. @satellite73

Answer 5

eh decomposition en element simple lol

Answer 6

to find \(A\) do this
cross out the factor of \(x-6\) in the denominator of \(\frac{-6x}{(x-6)(x+3)}\) and replace \(x\) by \(6\)
in other words visualize it as
\[\frac{-6x}{\cancel{(x-6)}(x+3)}\] and then where you see an \(x\) replace it by \(-6\) to get
\[\frac{-6\times -6}{-6+3}=\frac{36}{3}=12\]

Answer 7

and the answer whould be ?

Answer 8

would*

Answer 9

well that was wrong wasn't it

Answer 10

the answer is work little bit hehe

Answer 11

should have said replace \(x\) by \(\huge 6\)

Answer 12

yes should be 6 not -6

Answer 13

\[\frac{-6x}{\cancel{(x-6)}(x+3)}\]\[\frac{-6\times 6}{6+3}=\frac{-36}{9}=-4\]

Answer 14

then do the same thing to find B cross out the factor and replace \(x\) by \(-3\) (yeah i am sure this time\[\frac{-6x}{(x-6)\cancel{(x+3)}}\]
\[\frac{-6\times 3}{-3-6}=2\]