Question

Find the roots of the equation
$\frac{1}{x+4}+\frac{1}{x-7}=\frac{11}{90}$, $x\ne -4,7$

Answer 1

$\frac{1}{x+4}+\frac{1}{x-7}=\frac{11}{90}$

$\Rightarrow \frac{x-7+x+4}{(x+4)(x-7)}=\frac{11}{90}$

$\Rightarrow \frac{2x-3}{x^2-7x+4x-28}=\frac{11}{90}$

$\Rightarrow 90(2x-3)=11(x^2-3x-28)$

$\Rightarrow 180x-270=11x^2-33x-308$

$\Rightarrow 11x^2-(33+180)x-308+270=0$

$\Rightarrow 11x^2-213x-38=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{213\pm \sqrt{47041}}{2\left(11\right)}$

$x=\frac{213\pm 216.89}{22}$

So $x=214.945,-1.945$.