Question

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

Answer 1

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

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

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

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

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

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

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

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

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

$x=1$ or $x=2$