Question

I don't understand how to go from Step 1 to Step 2.
Equations below.

Answer 1

\[\frac{ dx }{ x(2-x) }=dt\]
and this is equivalent to:
\[\frac{ dx }{ x } + \frac{ dx }{ 2-x }=2dt\]
Please tell me why that is!

Answer 2

my guess, without computing, is that it is partial fractions

Answer 3

dis is partial fraction.u will get dis in integration chapter.just read the theory and example part.

Answer 4

\[\frac{1}{x(2-x)}=\frac{A}{x}+\frac{B}{2-x}\] and my guess is that \(A=B=\frac{1}{2}\)

Answer 5

in fact i can see it
eyeball the answer and you will get it

Answer 6

Thank you. Is this partial fraction covered in Calculus I or II? I have seen it done before but didnt know that it was called partial fraction.

Answer 7

in this type of problem u have to devide it in 2 parts.first fraction contains A and second one contains B

Answer 8

often this is a technique taught in pre-calc, but forgotten until calc 2 when you integrate

Answer 9

I see. Should I be able to find this in Paul's math notes? Thank you both.

Answer 10

Found it.