Alg5.1.16

If $\frac{A}{x}+\frac{Bx}{x^2+1}=\frac{5x^2+2}{x^3+x}\,$ what is the value of B.

Given, $\frac{A}{x}+\frac{Bx}{x^2+1}=\frac{5x^2+2}{x^3+x}\,$

Equating the numerators on both sides, we get

$5x^2+2=A(x^2+1)+Bx^2\,$

Equating the coefficients of $x^2\,$ and constants on both sides,we get

$A+B=5,A=2\,$

Hence the value of B is $3\,$