Question

Determine a possible value of $x$ if $6-\frac{6}{x}=x+13$, and $x\ne 0$.

• A. $-7$
• B. $-1$
• C. $1$
• D. $3$

Answer 1

The correct option is B $-1$

Given, $6-\frac{6}{x}=x+13$

$\Rightarrow 6x-6=x^2+13x$

$\Rightarrow x^2+13x-6x+6=0$

$\Rightarrow x^2+7x+6=0$

$\Rightarrow x^2+6x+x+6=0$

$\Rightarrow x(x+6)+1(x+6)=0$

$\Rightarrow (x+6)(x+1)=0$

Therefore $x=-1$ or $x=-6$