How do you express $(4x-2) /( 3(x-1)^2)$ in partial fractions?

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Answer 1 · 2016-11-23T07:29:16

The answer is $=(2/3)/(x-1)^2+(4/3)/(x-1)$

Let's do the decomposition into partial fractions

$(4x-2)/(3(x-1)^2)=1/3(A/(x-1)^2+B/(x-1))$

$=1/3(A+B(x-1))/(x-1)^2$

Therefore,

$4x-2=A+B(x-1)$

Comparing the coefficients of x,

$4=B$

Let $x=1$

$2=A$

Therefore,

$(4x-2)/(3(x-1)^2)=1/3(2/(x-1)^2+4/(x-1))$

How do you express (4x-2) /( 3(x-1)^2)(4x-2) /( 3(x-1)^2) in partial fractions?