Question

Put this in partial fractions:

\[1 \over y(4-y)\]

Answer 1

@NotSObright

Answer 2

\[\frac{1}{y(4-y)}=\frac{A}{y}+\frac{B}{4-y}\]

Answer 3

Combine fractions on right hand side so that you will have same denominator => numerators must be same

Answer 4

\[\frac{1}{y(4-y)}=\frac{A(4-y)+By}{y(4-y)}\]

Answer 5

\[1=A(4-y)+By\]

Answer 6

\[1=4A-Ay+By\]
\[1=4A+y(-A+B)\]

Answer 7

That's where I got... don't know how to carry on

Answer 8

\[4A=1 , -A+B=0\]

Answer 9

Constants on both side set them equal
set the coefficients of y on both sides equal
and so on...

Answer 10

Multiply both sides by y and let y=0
\[
\frac{1}{y(4-y)}=\frac{A}{y}+\frac{B}{4-y}\\
A= \frac 1 4
\]
Multiply both sides by4- y and let y=4
\[
\frac{1}{y(4-y)}=\frac{A}{y}+\frac{B}{4-y}\\
B=- \frac 1 4
\]

Answer 11

This is called the cover-up method.

Answer 12

Why aren't they both 1/4? With Zombie's method, they'd both equal 1/4

Answer 13

Sorry
\[B= \frac 1 4
\]

Answer 14

OK Thanks :)