Question

Solve the following quadratic equation:
$\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30},x\ne 4,7$

Answer 1

Consider the given equation.

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

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

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

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

$\Rightarrow (-11)\times 30=11(x^2-3x-28)$

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

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

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

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

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

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

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

$\therefore x=1,2$

This is the required solution.