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

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Answer 1 · 2018-05-19T18:29:47

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

Here,

$(1)(x+2)/(x(x-4))=1/2[(2x+4)/(x(x-4))]$

$color(white)((x+2)/(x(x-4)))=1/2[(3x-(x-4))/(x(x-4))]$

$color(white)((x+2)/(x(x-4)))=1/2[(3x)/(x(x-4))-(x-4)/(x(x-4))]$

$color(white)((x+2)/(x(x-4)))=1/2[3/(x-4)-1/x]$

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

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

$=>x+2=Ax+B(x-4)$

Take ,

$x=4=>4+2=A(4)=>4A=6=>A=3/2$

$x=0=>0+2=B(-4)=>B=-2/4=-1/2$

Subst. values of $A and B$ into $(2)$

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

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

How do you express (x+2) / (x(x-4)) (x+2) / (x(x-4)) in partial fractions?