Question

If $x+\frac{a}{x}=b$ then the value of $\frac{x^2+bx+a}{b{x}^2-x^3}$ is

• A. $\frac{6b}{a}$
• B. $\frac{5b}{a}$
• C. $\frac{2b}{a}$
• D. $\frac{4b}{a}$

Answer 1

The correct option is C $\frac{2b}{a}$

Given $x+\frac{a}{x}=b$ Multiply by x both sides

$x^2+a=bx$

$\Rightarrow x^2-bx+a=0$

So $\frac{x^2+bx+a}{b{x}^2-x^3}=\frac{x^2-bx+a+2bx}{-x(x^2-bx)}=\frac{0+2bx}{-x(-a)}=\frac{2bx}{ax}=\frac{2b}{a}$