Question

The product of the solutions of the equation $\frac{3}{x}=\frac{8}{x-3}-1$ is

• A. $-6$
• B. $-9$
• C. $9$
• D. $10$

Answer 1

The correct option is B $-9$

Given equation is :

$\frac{3}{x}=\frac{8}{x-3}-1$

On simplifying, we get
$3(x-3)=x(8-x+3)$
$3x-9=11x-x^2$
$x^2-8x-9=0$
$x^2-9x+x-9=0$
$(x-9)(x+1)=0$
$x=9$ and $x=-1$.
$\therefore$ product of the solutions is $\left(9.\right(-1\left)\right)=-9$