Question

If $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}(x\ne 3,-5)$, then $x$ is equal to

• A. $-9,7$
• B. $2,3$
• C. $2,1$
• D. None of these

Answer 1

The correct option is A $-9,7$

Given equation is: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}$

$\Rightarrow \frac{x+5-(x-3)}{(x-3)(x+5)}=\frac{1}{6}$
$\Rightarrow \frac{x+5-x-3}{x^2+2x-15}=\frac{1}{6}$

$\Rightarrow \frac{8}{x^2+2x-15}=\frac{1}{6}$

$\Rightarrow 48=x^2+2x-15$

$\Rightarrow x^2+2x-63=0$
$\Rightarrow x^2+9x-7x-63=0$
$\Rightarrow x(x+9)-7(x+9)=0$
$\Rightarrow (x+9)(x-7)=0$
$\Rightarrow x+9=0$ or $x-7=0$
$\Rightarrow x=-9$ and $x=7$

Hence, $x=-9,7$ are the required solutions.