Question

Find the roots of (P.S)
$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}x\ne -4,7$.

Answer 1

$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$

$\Rightarrow$ $\frac{x-7-(x+4)}{(x+4)(x-7)}=\frac{11}{30}$

$\Rightarrow$ $\frac{x-7-x-4}{x^2-7x+4x-28}=\frac{11}{30}$

$\Rightarrow$ $\frac{-11}{x^2-3x-28}=\frac{11}{30}$

$\Rightarrow$ $\frac{-1}{x^2-3x-28}=\frac{1}{30}$

$\Rightarrow$ $-30=x^2-3x-28$

$\Rightarrow$ $x^2-3x+2=0$

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

$\Rightarrow$ $x(x-2)-1(x-2)=0$

$\Rightarrow$ $(x-2)(x-1)=0$

$\Rightarrow$ $x-2=0$ and $x-1=0$

$\therefore$ $x=2$ and $x=1$