Question

If $\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x+4}$, then x could be

• A. $0$
• B. $-1$
• C. $-2$
• D. $-3$
• E. $-4$

Answer 1

The correct option is C $-2$

The given expression $\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x+4}$ can be solved as follows:

$\frac{1}{x}-\frac{1}{x+1}=\frac{1}{x+4}\Rightarrow \frac{x+1}{x(x+1)}-\frac{x}{x(x+1)}=\frac{1}{x+4}\Rightarrow \frac{x+1-x}{x(x+1)}=\frac{1}{x+4}\Rightarrow \frac{1}{x(x+1)}=\frac{1}{x+4}$

$\Rightarrow x+4=x(x+1)\Rightarrow x+4=x^2+x\Rightarrow x^2+x-x-4=0\Rightarrow x^2-4=0$

$\Rightarrow x^2=4\Rightarrow x=\pm \sqrt{4}\Rightarrow x=\pm 2$

Hence, $x=-2$