Question

Solve for $x$: $x(x-\frac{5x+6}{x})=0$

• A. $1$
• B. $-6$
• C. $-1$
• D. $3$

Answer 1

Answer: (C)

$-1$

$\{6,-1\}$: Distribute the multiplication by $x$. Note that, when you cancel the $x$ in the denominator, the quantity $5x+6$ is implicitly enclosed in parenthesis!
$x(x-\frac{5x+6}{x})=0$
$x^2-(5x+6)=0$
$x^2-5x-6=0$
$(x-6)(x+1)=0$
$x=6$ or $-1$
Note also that the value $0$ is impossible for $x$, because $x$ is in a denominator by itself in the original equation. You are not allowed to divide by $0$. Do not look at the product in the original equation and deduce that $x=0$ is a solution.