Question

Solve the following equation:

$\frac{1}{x-1}-\frac{1}{x}=\frac{1}{x+3}-\frac{1}{x+4}$

• A. $1\frac{1}{11}$
• B. $-1\frac{1}{4}$
• C. $-1\frac{1}{2}$
• D. $1\frac{1}{7}$

Answer 1

Answer: (C)

$-1\frac{1}{2}$

Given, $\frac{1}{x-1}-\frac{1}{x}=\frac{1}{x+3}-\frac{1}{x+4}$
$\Rightarrow \frac{x-x+1}{x(x-1)}=\frac{x+4-x-3}{(x+3)(x+4)}$
$\Rightarrow \frac{1}{x(x-1)}=\frac{1}{(x+3)(x+4)}$
$\Rightarrow x^2-x=x^2+3x+4x+12$
$\Rightarrow -8x=12$
$\Rightarrow x=-\frac{12}{8}$
$\Rightarrow x=-\frac{3}{2}$
$\Rightarrow x=-1\frac{1}{2}$