Question

Write the partial fraction decomposition of the rational expression. Check your result algebraically.

5x divided by (x-4)^2

and put it step by step how did you get it.

Answer 1

\[\frac{5x}{(x-4)^2}\]?

Answer 2

Yes

Answer 3

\[\frac{5x}{(x-4)^2}=\frac{A}{x-4}+\frac{B}{(x-4)^2}\] is step one

Answer 4

i meant add on the right

Answer 5

i guess now you have to multiply that mess out

Answer 6

what does A and B stand for? I have not learn this yet.

Answer 7

ooooh big mistake, ignore me
lets try again

Answer 8

oh okay haha

Answer 9

ok do you know what the goal here is? what you answer is supposed to look like?

Answer 10

Uh..sadly no. My teacher have not teach me this. I believe.

Answer 11

you job is to make the expression on the left look like the expression on the right
i.e. you goal is to find A and B that make this work
\[\frac{5x}{(x-4)^2}=\frac{A}{x-4}+\frac{B}{(x-4)^2}\]

Answer 12

A and B are some numbers, some constants, and your job it to find them

Answer 13

Oh, okay.

Answer 14

So, how do you find it?

Answer 15

if you add up on the right, you get a numerator of
\[A(x-4)+B\]

Answer 16

in other words, if you add on the right you get
\[\frac{5x}{(x-4)^2}=\frac{A(x-4)+B}{(x-4)^2}\] this tells you that
\[A(x-4)+B=5x\]

Answer 17

multiply and see that
\[Ax-4A+B=5x\] which means that \(A=5\) and since \(A=5\) and \(-4A+B=0\) you get \(B=20\)

Answer 18

some of these steps might be confusing, if so let me know
but the final answer is
\[\frac{5x}{(x-4)^2}=\frac{5}{x-4}+\frac{20}{(x-4)^2}\]

Answer 19

Thank you so much! I really understand it now!

Answer 20

yw