Question

write the partial fraction decomposition for the rational expression.
(2x-3)/(x-1)^2

Answer 1

We have a repeated linear factor, so we have to write it like this :D
\[\large \frac{ 2x-3 }{ (x-1)^2 }=\frac{ A }{ x-1 }+\frac{ B }{ (x-1)^2 }\]
Do you understand the initial setup? :D

Answer 2

yess i got that so far

Answer 3

Multiplying through by the denominator on the left gives us...
\[\large 2x-3=\frac{ A(x-1)^2 }{ (x-1) }+\frac{ B(x-1)^2 }{ (x-1)^2 }\]
\[\large 2x-3=A(x-1)+B\]

Answer 4

i got 2x-3 = A(x-1)^2 + B(x-1) because i multiplied the whole equation by (x-1)(x-1)^2

Answer 5

Hmm that's too many powers <:O You don't need that repeat to deal with the denominator. If you multiplied through by that, then on the right side you would be left with:
(2x-3)(x-1) Since you cleared the denominator AND THEN SOME :D

Answer 6

ok got it