The partial fraction decomposition of 62x/8x^2−10x+3 can be written in the form of f ( x ) 2 x − 1 + g ( x ) 4 x − 3 f(x)=? g(x)=?

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Answer 1 · 2018-05-14T18:41:21

The answer is #f(x)=-31# and #g(x)=93#

Perform the decompositio into partial fractions

#(62x)/(8x^2-10x+3)=(f(x))/(2x-1)+(g(x))/(4x-3)#

#=(f(x)(4x-3)+g(x)(2x-1))/(8x^2-10x+3)#

The denominators are the same, compare the numerators

#62x=f(x)(4x-3)+g(x)(2x-1)#

Let #x=1/2#

#=>#, #31=f(x)*-1#

#f(x)=-31#

Let #x=3/4#

#=>#, #93/2=g(x)/2#

#g(x)=93#