Question

Find the roots of the following equations:
(ii) $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne -4,7$

Answer 1

(ii) $\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}$
$\Rightarrow \frac{x-7-x-4}{(x+4)(x-7)}=\frac{11}{30}$
$\Rightarrow -\frac{11}{(x+4)(x-7)}=\frac{11}{30}$
$\Rightarrow (x+4)(x-7)=-30$
$\Rightarrow x^2-3x-28=-30$
$\Rightarrow x^2-3x+2=0$
$\Rightarrow x^2-2x-x+2=0$
$\Rightarrow x(x-2)-1(x-2)=0$
$\Rightarrow (x-2)(x-1)=0$
$\Rightarrow x=1or2$